It appears Jesus did heal everyone who asked, and even those who did not ask, but WHY? The New Testament gives us many examples of Jesus and the apostles healing others. When Jesus healed, He did so for those with and without faith. The (Roman) centurion asked for his servant to be healed (Matt 8:8-13). We do not know the amount of faith this servant had, but we know he was not Jewish. Jesus also healed 10 lepers (see Luke 17:12-18), however, only one had enough faith to praise God and thank Him. He also healed those who would do him harm, as in the high-priest's servant whose ear was cut off. (Luke 22:49-50). If faith was not a prerequisite for the healing, Jesus must have had a higher purpose.
In addition, we know of no instances in scripture where apostles used healing for each other. In fact, Paul tells Timothy to take a little wine for his stomach (1 Timothy 5:23). We know that Paul was blinded on his way to Damascus and received only part of his sight back. He inquired of God three times to heal his vision, but ultimately he recognized that he was better able to do God's will with his infirmity. He accepted the Lord's will regarding the "thorn in his flesh" and that God's strength was made perfect in Paul's weakness (2Cor 12:7-10). Does this mean Paul lacked faith because he was not fully healed? Why didn't Paul to ask Peter or one of the other apostles to heal his vision?
It appears that in Jesus's day, healing was used as a witness of God's power – to unbelievers that they might become believers; and to believers that they might strengthen their faith. But once the holy spirit was poured out at Pentecost, it seems the primary reason for healing was to convert unbelievers.
We believe that the greater purpose of physical healing is that it is symbolic of the healing from sin that comes only through Christ. By his stripes we are healed (Isa 53:5). Jesus died as the ransom (corresponding price) for Adam and all of Adam's children. 1 Corinthians 15:22 For as in Adam all die, even so in Christ shall all be made alive. This is the healing we as Christians should be praying for and rejoicing over.
Rather than ask God for healing of physical infirmities, we think the faithful Christian should be asking for more strength and faith to endure the physical infirmities, and that the infirmity will increase the fruits of the spirit and enable us to be more Christ-like.
2 Corinthians 12:9 And he said unto me, My grace is sufficient for thee: for my strength is made perfect in weakness. Most gladly therefore will I rather glory in my infirmities, that the power of Christ may rest upon me.
For a more comprehensive look at healing in the scriptures, we recommend listening to this radio program: http://www.christianquestions.com/858-are-christians-supposed-to-be-healed/.