Every human being has been born in sin, and all of us are suffering the effects of the curse of sin. The ultimate effect of sin is death. This is the last enemy to be destroyed (1Cor.15:21-28). Jesus died to redeem us from sin, sickness and death (Gal.3:13). It is important, however, to understand the kingdom theology of the 'already' and the 'not yet' [refer to the writings of George Elton Ladd and Gordon Fee].
* 'Already' sin has been atoned for but 'not yet' do we see sin completely eradicated from the world or our lives.
* 'Already' death has been defeated but 'not yet' do we see death totally destroyed.
* 'Already' sickness has been taken by Jesus himself, but 'not yet' do we see sickness totally removed from the earth or our lives.
* 'Already' Satan is a defeated foe, but 'not yet' do we see his final punishment and judgment.
The second coming of Jesus will complete and finalise all that Jesus began at his first coming. Then there will be an age without sin, sickness, suffering, death or Satan's opposition.
Right now we are all getting older (graying, less agile, more frail, etc). Unless the Lord comes back in our lifetime (which he may), we will all die of something. The heart will stop beating sometime. Only the final generation will escape death in this life (1Thess.4:15-18). However, in reality, for the believer, death is ultimate healing! To be absent from the body is to be present with the Lord. Also, healing is not permanent. As far as we know, all people whom Jesus Himself healed eventually died.
Sometimes God heals and sometimes He does not. Jesus did not heal everybody. No person can give any fixed answers as to why. Only God Himself knows. He does what He does because He is God.Our responsibility is to pray and ask God to heal and help us (Jas.5:13-16), then to trust God with the outcome. Our attitude is not one of fatalism (“What will be, will be”), but one of faith (“We trust You, Lord, whether you deliver or not!”). When it comes to healing, let's have the attitude of the three Hebrew children who were facing a fiery furnance – "God is able to heal … God will heal … but even if not, we will still serve him (Dan.3:17-18)!"
P.S. For further helpful teaching on the subject of healing, I highly recommend the book Power Healing by John Wimber.