The problem of why some are not healed has been written about and discussed by many, many people much more intelligent and gifted than me. So I do not even imagine that I have anything new to offer in the quest for trying to understand the ways of God.
As with all spiritual matters, we all read and listen to the thoughts of others and to God's Word in the Bible and His word through the leaders of the Church, both present and past, and then come to our own acceptance of what we think might be the truth.
I have prayed for myself and others for many, many years. After all this time, it's still puzzling to me why some people are healed instantly or very quickly and others are not healed at all (at least in an obvious way). Especially puzzling is when the obviously innocent suffer, such as babies or young children. In older children and adults, we can at least think that perhaps the suffering is being used as a discipline to help them to grow spiritually or to be better persons. But that doesn't apply to the little ones.
Because of God's revelation in the Bible and through the life of Jesus, we know that God is love; that He loves all those He has created; that He grieves over our suffering and is with us as we go through it. But we also know that God has the power to take away that suffering, in the blink of an eye.
We who are parents know how the suffering of our children pains us; that if there were anything we could do, including dying for them, we would not hesitate. Is not God the very best of fathers; the perfect Father?
When I mull over these age-old questions, or tire of praying for the same thing over and over for years and years, I always come back to the same thing--the Cross. Jesus suffering and death on the cross did not make sense at the time. Even Jesus prayed to the Father in the Garden of Gethsemane to be saved from the suffering of crucifixion and death, knowing that the Father had the power to change the circumstances. But God the Father said no. And it was only after the Resurrection that the understanding came of why He had to suffer and die in such a cruel way.
So it is with us. Sometimes we can see the good fruit of suffering here on earth. But most of the time we will not understand until after we pass on.
I once visited one of the cathedrals in Paris, France (I've forgotten which one) where there was a Pieta; not a duplicate of the one in Notre Dame, but similar. In this one the Blessed Mother was holding the dead body of Jesus, but instead of looking down at Him she was looking up to Heaven. It was as if she were asking, "Why?" It reminded me of all mothers who have lost a child, but also of all of us. Someday we will know.