Is it Harder to Heal Believers or Non-Believers?

I have been struggling with this question for several months now, especially in light of the results of prayer I've seen. Healing seems to be a long process for believers for whom I've prayed. Is it even possible for a believer to receive an instant-healing miracle through a prayer of faith?

Perhaps God deals with His children differently than He does the world. Jesus said that [instant] healing would be a sign for the world so they would know that the LORD is God (see Mark 16). Since Christians no longer need to be convinced that the LORD is God, perhaps God's main goal isn't to instantly heal them as a sign, but instead to teach them how to be more reflective of His image by understanding His ways more deeply. Notice that James instructs sick believers (perhaps the immature in Christ who do not know the LORD's benefits) to call the elders (who are the mature in Christ) to pray in faith over them (see James 5). This would be a perfect opportunity for the elders to teach sick believers the promises of God and then to display the principles of spiritual warfare through their prayer of faith. Thus, it seems to me that God set it up so that His children would learn His ways through the process of healing.

So what could God want His children to learn through their pursuit of healing? Perhaps it is simply the fact that God is willing to heal us. Or perhaps God wants to teach us that we need to take the spiritual realm seriously, and that it can affect us physically (as well as emotionally and spiritually) for better or for worse. Perhaps God wants us to know that He has granted us access to physical healing--just as to forgiveness of sins--through the atonement, or that healing comes through proper celebration of communion. Perhaps God wants us to realize that we are supposed to be seeking Him above all else and that He will do great things for us if we love Him and obey His commands (see Psalm 91). God desires the best for His children. Certainly, knowledge of His benefits would be nothing but good for us.

My conclusion for the moment is that God may very well heal believers instantly, but if He doesn't, perhaps He is calling those particular people into a higher level of intimacy with Him that requires them to learn something new. Of course, if the person praying the prayer of faith is not acquainted with (or proficient at implementing) God's healing methods, the sick person may not recover simply because the sickness was not defeated. As for me, I am going to be particularly careful not to blame anyone's sickness on anyone but the devil and his minions, and I will continue to seek God so that I can accurately reflect Him to everyone I encounter.