I've experienced ~40 hours now with no pop-ups. I do not know why.
It has occured to me that if the ISP mail server asks for authentication, and it counts time-out before the password sent by Mail reaches it, then the server sends a message back to Mail notifying that the authorization failed.
It could be that Mail is designed to keep things simple for us users (ya think?!) and instead of posting an alert that the connection timed-out, it simply invokes the pop-up so the user can try again.
If that is the case, then it should be the ISP's responsibility for setting the time-out window too short.
But that is tricky, too. They can't leave the authentication window open forever. It's likely there is standard protocol for this in order to assure interoperability between various servers and clients.
If heavy network traffic or other factors increase the latency between when the serve makes the request and the answer from Mail arrives then a time-out could occur even when no party changes any software or settings on their own end.
Who knows -- with the recent patches being applied across the net for DNS security in recent weeks perhaps the time-outs are being exceeded more frequently. And just as 'perhapsly' the IT crews are managing to fine tune performance again so that any latencies introduced by the patches are being overcome.
All of that could account for the randomness we've been experiencing.
Just thinkin. I may be full of prunes.
Here's a MacFixIt article that nicely summarizes ideas to try if you have the problem:
http://www.macfixit.com/article.php?story=20080805080357126
Unless you are a MacFixIt member it's probably only free online for a day or so. It's title focuses on MobileMe mail, but the circumstances generally fit the symptoms describe by people in this thread who may or may not have MobileMe, Comcast, etc.
Hope it helps -sailhome
