Christians believe that God answers prayers and does miraculous healings...but why does he never ever heal an amputee?

Because they lack faith

I don't know if this is a valid answer to your question, but I'll give you some of my thoughts on it.
First of all, I very much believe in the power of prayer, believe in God and that His son Jesus came came and was sacrificed for the forgiveness of my sins and to give me eternal life in heaven after my earthly life is over.
I know many people pray when they are in need of something. Whether it be healing or money or strength, etc., to deal with something we feel we cannot handle on our own. In fact, we are beggars. Many pray to beg God for His services and His divine intervention to our needs. The Bible does state, "Ask and it shall be given unto you, but it is His will that will be done. You can pray for anything, but sometimes, (for reasons known only to God,) the answer is not what you want or expect.
I have also noticed that many people will never hesitate to pray or beg God for something, but how often do we pray or talk to God without asking for something? How often do simply talk to God to say "thank you?" Maybe, if we thanked God more often for what we have and what He has given us, some of things we pray for would be given to us.
Lastly, I think many do not realize that what we pray to or ask God for, may be given to us in ways that we do not expect. For example, if you pray for strength, you just may get more problems which in turn will make you stronger. If you pray for patience, you may get situations that will test you, pushing your patience to the limit.
Anyway, I know this probably did not answer your original question, but maybe I gave you a few things to think about and consider.

Those are called "creative miracles" - I have heard of them happing when I watched GodTV.

From the point of view of an atheist...

Some Christians might answer that God doesn't provide miracles just because someone believes and asks; he has a purpose and plan which has a far wider scope than any human could grasp, and it may be that he caused the amputation because that person had a specific spiritual journey that required a disability in order to learn.

(I actually know someone with a similar view, A man who was paralysed for the C7 vertebra down, no longer able to get around without a wheelchair. He lost the ability to have erections. But he said it was the best thing that ever happened to him. He had been a promiscuous player who used women. Through his disability, he learned how to have an emotional orgasm in his brain, how to give a woman pleasure, and how to have an intimate and long lasting relationship with deep love. He said he'd never give that up or trade it for anything.)

But as for the rest of the "miracle" cures of things that can go into spontaneous remission - we now know that the mind, emotions and body are not separate but one-in-the-same, even down to the levels of molecules, atoms and electrical charges. Thus, what a person believes at the deepest levels of the unconscious has a profound effect on their bodily chemistry and all internal processes. Christians and other theist might not believe it - but certainly we know that the placebo effect accounts for about one third of all healing.

But he allows you to speak

I did not know he healed these people you have indicated.

They are praying to the wrong being! It has been well established that Gangleslotte came to Earth and disguised himself as the fictional being Yahweh in order to lead the followers of Farblesnozz astray!

According to the Jesus character, you are supposed to chop off your body parts and gouge out your eyes to keep from sinning So, why would you ever be able grow back missing body parts? All you would do is sin again.

Watch , soul surfer.
Not everything is only one way. Maybe needs a different healing besides the obvious.
Just an idea or a possible different point of view.

Maybe worms pray with greater belief and sincerity?

As it is known that they actually regenerate body parts.

😀

The Lord knows his own.

You know how it is. God answers all prayers. It's just that sometimes the answer is "No."

Never forget Voltaire’s all purpose explanation,

“God’s only excuse is that he does not exist ”

We'll never know!

There are very, very few animals that can regrow a lost limb, at least to some extent, so it's not just us.

Look up Miracle of Calanda. Although there is a question as to whether the guy was actually an amputee.

I think He does when a person's cancer goes into remission as an example