What we have to realise is that although God is able and willing to heal the sick, instant healing is by no means automatic. If it was, there would have been no instances in the Gospels when Jesus did not heal everyone. He healed only one person at the pool of Bethseda when there were many sick people there. He must have passed the Gate Beautiful many times while the lame man was there begging, but He never healed him. That was left to Peter and John. Jesus could not heal many people in His home town because of their unbelief.
Jesus said that He could do nothing of Himself. He did only what the Father was doing. So, when the Father wanted to heal sick people, Jesus was then able to heal them. He was totally dependent on the Holy Spirit to perform miracles because He had agreed with the Father to lay aside His divine attributes when He was incarnated, and only received them back when He sat down at the right hand of the Father after His ascension. So, while He was on earth, He depended on the same Holy Spirit whom we depend on; with the difference that He did it a lot better than us.
Jesus said that we cannot do anything without Him. So, healing is up to His sovereign will. If we pray for a person and they are not healed it is because Jesus has not decided to heal that person for reasons only known to Himself. He would have good reason not to heal someone, because healing is something He does naturally out of his compassionate nature. He is always able and willing to heal, but there are hindrances and reasons why He does not heal every time.
Unbelief could be a factor, but not always in the individual. He has healed people who did not demonstrate any faith. A whole church movement or denomination could be unbelieving and cessationist, so Jesus would not be able to heal anyone in those churches, not matter how willing and able he is to heal them.
Sin could be another factor. Wrong relationships, unforgiveness, lack of honouring of parents, and all sorts of other garbage could prevent healing.
Demonisation could be another factor. Many people are healed after being delivered of a demon influence in their lives.
You may not be the right person to pray for the sick one. God may want to use someone else to bring healing to that person.
It may not be the right time for that person to be healed. Jesus demonstrated through a healing of a man who had been blind from birth. He said that the blindness was there until the time of healing so that God would be glorified by the healing.
The healing of the lame man by Peter and John caused 5000 new converts for Christ.
It may be that God is wanting to use a particular doctor to bring about the healing through medical intervention.
The practice of some Pentecostal groups that teach that people should not go to the doctor can cause unnecessary suffering and even early death. These groups teach that it is a lack of faith to go to the doctor. This is wrong. Faith is using all the resources that are available to us to being healing.
We have to accept that death is sometimes the ultimate healing for a person.
When we pray for someone, we are putting our dependence on a sovereign God. Therefore we can pray with freedom and not have to take the blame for when a person is not healed. The sick person doesn't have to take the blame either.
John Wimber prayed for thousands of sick people and his statistics told him that only 25% got instantly healed, and most of them were in the evangelistic context. 50% had different rates of improvement in their condition, and 25% were never healed and they were cured either by medicine or they died.
Jesus is the potter and we are the clay. We do not tell our God what He is to do. That would be pride and arrogance. But putting our faith in the hands of God to do whatever He wants according to His will, has to cause a major positive difference in a person's life whether he or she gets healed or not.
After learning this, I have a lot more confidence in praying for the sick, and even developing a healing ministry, because the fear of failure has been removed from me, and I can put my trust in a sovereign God who loves us and wants the best for us.
Oh, by the way, don't believe any of that rubbish about sickness as a way of Christians bearing their cross of suffering. The Scripture does not teach that. Scriptural suffering is about persecution, not sickness.
It is amusing to me to hear of a "spiritual" Christian holding forth that their sickness is their special cross that they are bearing for God to teach them how to come closer to Him, and yet they are rushing down to the doctor's surgery to get medicine or to the hospital for an operation to get cured.
Absolute nonsense and hyprocrisy.