the difference in english is: perché non mi rispondi - why don't you answer me? perché non rispondi - why don't you answer?

wrong my Italian mates:). In this sentence, we add "mi", if we want to emphasise/stress the subject. Especially if you are angry with the listener.

maybe you can use "perché non mi rispondi" it's more common.

50% chance of using any of the two, really.