Apple's Income Mail Stopped Working
Enthusiast - Level 2

My wife's i-Mac was working OK (usually) with Apple's Mail application. Periodically it would request a password, but that was rare. For the past 4-5 days, it just will not go away. She repeatedlly adds her password, and it just ignores it. She can send mail, but cannot receive any email. I've heard of major Verizon problems with Mac, but this is really weird. I have another Mac that does this once in awhile, but will usually start working again when I plug in my password.

What to do? What to try?

Thanks much.