"I believe in Divine healing. I would like to know why some people experience  sickness come back again .and why some are not healed."

ANSWER:
Good question, Molly.  That's actually two questions: 1) why does sickness return and 2) why are some not healed?  Let's take them in order.
1)  Why does sickness return?  Sickness can return for basically two reasons:
     a)  When Jesus healed the cripple man at the pool of Bethesda (you'll find the story in John 5:1-14), He later ran into him in the temple and told him "Behold, thou art made whole: sin no more , lest a worse thing come unto thee."  So we can see that sometimes after God heals someone, they open the door to the devil to bring sickness back upon them by getting right back into sin.  And if they again get entangled in sin, sometimes they are worse off than before.  So what's the solution in this case? Repent and tell God you'll live your life for Him.  1 John 1:9 says If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
Run back to God if you sin, don't run away from Him; He loves you.
      b)  Sickness can come back again also because maybe they've been healed by the faith of someone else or maybe they were healed in a mass healing crusade where mass healings, sign and wonders were taking place.  Then when they get back home or back on their own, the devil can rob them of their healing by making them doubt; by bringing back a symptom or two.  Pretty soon that person will start saying, 'well, I thought God healed me but I guess he didn't.' ..., and the devil has got you!  You've just been deceived into believing the symptoms rather than God's Word.  What's the solution here? James 4:7 Submit yourselves therefore to God. Resist the devil, and he will flee from you. 
     How do you resist the devil? Submitting to God means submitting to His Word.  Jesus resisted the devil by saying, 'It is written', 'It is written,' 'It is written!'  When symptoms start to come back on you, just tell Satan, 'No you don't devil, you're not going to put that back on me in Jesus Name!  It is written, 'He was wounded for my transgressions, bruised for my iniquities; the chastisement of my peace was upon Him and with His stripes I am healed!'  (Isaiah 53:5)  Devil, you're a liar; take your lying symptoms and be gone in Jesus name!...and then stay in faith by praising God and worshipping God for your healing.  "Thank you Jesus for healing me.  You're so good.  I give you praise and honor and glory because I'm healed.  I'm not trying to get healed, I was healed over 2000 years ago and I'm taking advantage of it now.  Thank you for healing me Lord!" 
     Molly, that's how you keep your healing.  Refuse to believe the lying symptoms the devil is trying to bring against your body.  Resist the devil and he will run from you as in terror!  God inhabits the praises of his people (Psalms 22:3)

2)  Why are some not healed?  There are at least 4 reasons people are not healed.
          
           a)  When Jesus was in his own hometown of Nazareth, the Bible tells us in Mark 6:5 And he (that's Jesus) could there do no mighty work, save that he laid his hands upon a few sick folk, and healed them. Notice it doesn't say 'He wouldn't, it says He Couldn't)  Someone says, 'I thought Jesus could heal if He wanted to.'  The Bible says he couldn't!  Now why couldn't He?  Mark 6:6 tells us why: And he marvelled because of their unbelief..., Matthew's account of this same incident tells us again:  Matt 13:58 And he did not many mighty works there because of their unbelief.  You see, unbelief hinders Jesus.  After all, if you don't believe in Jesus, you can't be saved.  God's not going to usurp authority over your own will. Believing that Jesus died and rose again for you is your choice. 
     Now how is Jesus going to help their unbelief?  Let's look at the rest of Mark 6:6..., And he went round about the villages, teaching.  You see, teaching is the cure for this kind of unbelief.  Knowledge of God's Word is the cure for this kind of unbelief.  Heb 13:8 says: Jesus Christ the same yesterday, and to day, and for ever. If unbelief hindered Jesus then, unbelief will hinder Jesus now. By the same token, if Jesus healed then and He doesn't heal now, then He has changed.  NO!  Thank God, Jesus is still the healer today.  So one reason some fail to receive is unbelief, and secondly

          b)  They've never been taught HOW to receive.  Everything we will ever receive from God has to be by faith.  For instance, salvation: Eph 2:8 For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Salvation and faith are a gift of God.  God demands that we have faith:  Heb 11:6 But without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him.  If God demands that we have faith, how do we get faith?  Rom 10:17 So then faith cometh by hearing, and hearing by the word of God.  Faith is the same for every area of life.  If you need faith for salvation, find scriptures on salvation; if you need faith for healing, find scriptures on healing; if you need faith for finances, find what God has to say about finances.  When you need healing, that's not the time to be studying about the antichrist..., unless you get healed you're not going to be around when he gets here anyway!
FAITH IS SIMPLE!  Faith is not hard.  What do we mean by faith?  The Bible tells us in 2 Cor 4:13
We having the same spirit of faith, according as it is written, I believed, and therefore have I spoken; we also believe, and therefore speak;  Faith is believing and speaking.  Here's a Bible illustration:  Rom 10:9-10 9 That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved. 10 For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation.  So, the way we get saved is to confess with our mouth that Jesus is Lord and believe in our heart that God has raised Him from the dead...and what's the result?  SALVATION!  Notice that is the spirit of faith: believing in the heart (spirit) and confessing with the mouth.  Here's another Bible illustration:  Jesus said in Mark 11:23 For verily I say unto you, That whosoever shall say unto this mountain, Be thou removed, and be thou cast into the sea; and shall not doubt in his heart, but shall believe that those things which he saith shall come to pass; he shall have whatsoever he saith.
Notice the scripture tells us to SAY and NOT DOUBT...in other words, BELIEVE in your heart. 
Jesus, in the above passage mentions saying three times and believing only once.  People are not missing it as much in their believing as they are in their saying.  He tells us to speak to our mountain.., If you need healing, then sickness is your mountain.  Speak to it in Jesus' name and tell it to GO!  Jesus also tells in the very next verse: Mark 11:24 Therefore I say unto you, What things soever ye desire, when ye pray, believe that ye receive them, and ye shall have them.  That's also faith: believing you receive WHEN YOU PRAY!  Not after you pray sometime, not believe after you feel better, not after you feel your body to see if it's healed, not someday, somewhere, some how, some time later...believe you receive the minute you pray regardless of circumstances.  Believe God has heard and answered your prayer NOW.  That's what faith is and does.  God didn't make anything difficult for us.  Believing is receiving and receiving is believing.  Now thank Him for your healing.  1) Unbelief, 2)Not being taught how to receive and #3:

          c)  Not walking in Love:  Why is this important?  Gal 5:6 For in Jesus Christ neither circumcision availeth anything, nor uncircumcision; but faith which worketh by love .  Notice it says that faith works by love.  If you're not walking in love toward God and your fellow man, your faith won't work.  What do you mean, walk in love?  That's kind of life-long challenge.  I encourage you to meditate and practice the scriptures in the Amplified Bible in 1 Cor 13:4-8

4 Love endures long and is patient and kind; love never is envious nor boils over with jealousy, is not boastful or vainglorious, does not display itself haughtily.
5 It is not conceited (arrogant and inflated with pride); it is not rude (unmannerly) and does not act unbecomingly. Love (God's love in us) does not insist on its own rights or its own way, for it is not self-seeking; it is not touchy or fretful or resentful; it takes no account of the evil done to it [it pays no attention to a suffered wrong].
6 It does not rejoice at injustice and unrighteousness, but rejoices when right and truth prevail.
7 Love bears up under anything and everything that comes, is ever ready to believe the best of every person, its hopes are fadeless under all circumstances, and it endures everything [without weakening].
8 Love never fails [never fades out or becomes obsolete or comes to an end]...,
When you meditate that word, substitute the word I for Love...in other words say: I endure long and am patient and kind.  I never am envious or boil over with jealousy, etc.  I guarantee if you do that for 30 days, you'll have to pinch yourself to see if it's really you.
     Now if your saved or born again, Rom 5:5 the love of God is shed abroad in our hearts by the Holy Ghost which is given unto us.  Also John tells us in 1 John 3:14-15 We know that we have passed from death unto life , because we love the brethren. He that loveth not his brother abideth in death.  15 Whosoever hateth his brother is a murderer: and ye know that no murderer hath eternal life abiding in him.  So if you haven't received the Lord Jesus Christ into your heart, walking in love would be almost impossible.  Ask Jesus to come into your heart is the solution for walking in love.  After that you have to continue to yield to the Holy Spirit in your love walk.
So: #1 unbelief, #2 not being taught how to receive or about faith, #3 not walking in love and #4 and probably the most important (not necessarily the #1 reason, but the most important) is:

          d)  Not discerning the Lord's body.   What in the world does that mean?  This has to do about not seeing the significance of the taking of communion.  Paul writes to the Corinthians saying in 1 Cor 11:26-30  For as often as ye eat this bread, and drink this cup, ye do shew the Lord's death till he come.  27 Wherefore whosoever shall eat this bread, and drink this cup of the Lord, unworthily, shall be guilty of the body and blood of the Lord.  28 But let a man examine himself, and so let him eat of that bread, and drink of that cup.  29 For he that eateth and drinketh unworthily, eateth and drinketh damnation to himself, not discerning the Lord's body.  30 For this cause many are weak and sickly among you, and many sleep. 
          This is the only place in the New Testament that gives us a reason that many are weak and sick and many sleep or die prematurely.  What reason?  ...Not discerning the Lord's body.  To discern is to see.  We must see or know the significance of the blood and the body.  Hebrews tells us Heb 9:22
without shedding of blood is no remission and Heb 9:28 So Christ was once offered to bear the sins of many.  When Jesus went to that cross for us and poured out His blood for us, His blood was shed for our remission of sins.  What about His body?  His body was broken for our physical sustenance.  The Bible tells us (speaking of Jesus)
 
Isa 53:5 But he was wounded for our transgressions, he was bruised for our iniquities: the chastisement of our peace was upon him; and with his stripes we are healed.

Matt 8:17 That it might be fulfilled which was spoken by Esaias the prophet, saying, Himself took our infirmities, and bare our sicknesses.

1 Peter 2:24 Who his own self bare our sins in his own body on the tree, that we, being dead to sins, should live unto righteousness: by whose stripes ye were healed.

Isaiah prophesied that when Jesus would be offered on the cross that he would take care of our sins and sicknesses.  Matthew interprets Isaiah as saying that Jesus took our infirmities and bare our sicknesses.  Peter agrees and says that he bare our sins and by his stripes ye were healed. In other words, those Roman soldiers that beat Jesus laid on Him many stripes.  Those stripes were for our physical healing.  So Paul is saying in 1 Corinthians when we take communion, we have to discern or see that His blood was shed for our remission of sins, His body took those stripes for our physical healing.  If we don't discern that, if we don't see that we'll be weak and sick and might even die prematurely.  Jesus was our Passover Lamb.  Believe it.  Receive it.  Everything Jesus did was for you.  Receive Him as your Savior; receive Him as your Healer.  We have a twofold redemption through Jesus Christ.

So what's the summary?  Some don't receive healing because of:
#1 unbelief
#2 not being taught how to receive or about faith
#3 not walking in love
#4 not discerning the Lord's body