I think that Prospero renounces his magical powers for a variety of reasons. Here are some possible reasons why he would do this:
- He no longer needs his magic. For most of this play, he has wanted to use his magic to punish those who did him wrong and to get a better life for himself and Miranda. Now this is no longer necessary.
- Perhaps he feels that the power that the magic has given him has corrupted him. I think that he may feel that using magic to essentially enslave spirits like Ariel (as well as Caliban) is something that he should not continue to do.