Wayne Grudem takes, I think, a scripturally balanced view of this sensitive subject. To summarise:-
It is right to pray for healing, Mt 6:13; 3 Jn 2.
Jesus frequently healed all who were brought to him.
A high expectation of healing is implied in our regular use of ordinary medical remedies. We do not usually argue, “I won’t take this treatment, because it’s better for me to suffer than to be well!”
It is right to pray believingly for healing. James warns that unbelief can lead to prayerlessness and failure to receive answers from God, Jas 4:2.
However, when we pray for healing, our prime concern must be for God to be glorified in that situation, whether he chooses to heal or not.
We ought also to pray with the same kind of compassion that Jesus felt for those whom he healed.
We need to face up to the pastoral problem that can occur when we raise people’s expectations of miraculous healing and then nothing seems to happen. This can lead to disappointment and anger. It is at this point especially that we need to insist on the primacy of the gospel of salvation and to insist that this is the greatest gift of God and is available to all who believe. At any rate, we ought to avoid the following mistakes: (a) not praying for healing at all (this is disobedient to Scripture); (b) telling people that God rarely heals today (this does not provide an atmosphere conducive to faith); (c) telling people that God always heals today if we have enough faith (this is cruel and unscriptural teaching).
We can tell people that God can and does heal today, and that it is very possible that they will be healed. We need to point out, however, that we are living in tension between the ‘now’ and the ‘not yet’ of God’s kingdom. Therefore, people will in this life experience healing, but also continuing sickness and eventual death, 2 Cor 4:16. ‘In each individual case it is God’s sovereign wisdom that decides the outcome, and our role is simply to ask him and wait for him the answer.’ (Grudem)
1 Cor 12:9 speaks of ‘gifts of healings’. Those so gifted will find their prayers for healing answered more frequently and more thoroughly than those of others. When such gifts are identified, the church should provide encouragement and opportunities for the exercise of this ministry.
Sometimes God will grant special faith (Jam 5:15) that healing will occur. At other times, he may choose not to heal (cf. 2 Cor 12:7; 2 Cor 4:16; 1 Tim 5:23; 2 Tim 4:20). At such times, we need to remember the truth of Rom 8:28. We also need to learn to give thanks to God in all circumstances, 1 Thess 5:18. Scripture teaches a positive theology of suffering, Psa 119:67, 71.
Based on: Grudem, Systematic Theology, 1066-1069.