Mail won't remember email passwords

At least once a week Mail requires that I resubmit my email password to one or more of my email accounts. It may be new since an update, but it certainly wasn't the case earlier. I've had to change passwords so many times I couldn't even tell you what they are anymore, so each time this happens, they all get reset - again. I'm on a MacBook Air with the Yosemite 10.10.3 iOS.

It's getting old. Any thoughts? Advice?

Thanks!