Mail will repeatedly ask for my password - up to 15 times an hour.

I know the issue is not with Yahoo because I receive mail in real-time on my iPhone. Any idea what could be causing this and how to fix it? It happened a few months back and "spontaneously" went away, but now it's doing it again. Sometimes I won't even get the bouncing Mail icon - I'll think I have no new messages until I check my phone and see that I've had several going back an hour or so.