Why are some not healed?
Healings are given by the mercy of God, He’s not obliged to do them. We see Paul in 2 Corinthians 12:9 was not healed of his “thorn in the flesh” whatever that refers to. I know it sounds harsh but in some way it is better. For those to think that when people pray they didn’t will hard enough or God likes you less than that other guy in your church is more damaging to one’s faith to know that they come with a greater purpose in mind, not one we can scrawl down with a manual. Also if God always did miracles, this again would impose on our free will. If God always granted miracles also, whose to say we won’t start summoning God like a butler, thus killing the free-being relationship God has with his people.
So to the general answer as to why some aren’t healed, is I just don’t know. Some are healed even when they doubt anything would happen at all, others have all faith but nothing happens. We won’t be able to test-tube God, but that’s not to say we won’t observe some correlations in miracle data (See the article on Undeveloped countries with miracles, particularly the part about breaking of the kingdom).