joining this thread late (my first post) ...
If we think that the material world is all there is, and that there is nothing after death, then yes, it would appear that God not healing an amputee (or allowing it to happen in the first place) is terrible and makes no sense. This naturally leads to hating God and/or not believing etc. Completely understandable. And if people are convinced that there is only one life, and nothing happens after this life (or possibly, we have one life and then get judged on where we spend eternity), then i see virtually no argument that could answer the original questions adequately. It would lead to atheism being the only logical conclusion.
However, consider for a moment that this life is just one of many. That is, reincarnation. So, each life becomes a lesson designed to grow the real you, the soul. And, under this concept, if you consider having millions of lifetime experiences, then experiencing one or more lifetimes as an amputee (or rich person, poor person, woman, man etc.) may simply serve to provide a perspective as you gain wisdom and understanding. For me, reincarnation is the only thing that helps to make sense of all this.
Follow up question/answer may be, to what end are we trying to improve our souls? Consider that each soul comes from the exact same thing (God, Creation, source, whatever you want to call it), and that our goal in being temporarily separated from the source is to learn, experience and grow through countless life experiences and incarnations. With the ultimate goal to rejoin the original source, only to do it again and again. It's a giant wheel of life, only, what we experience with this body is a very small part if the big picture.
So talking about being an amputee, being healthy, being rich, or poor, or tall, short, white, black, man, or woman for a given lifetime is simply too narrow a discussion. It's like trying to understand a movie, by analyzing a single 5 second scene. It can't be done.