I have had (as have many other folks I know) this annoying issue of Mail.app suddenly throwing up a dialog asking for my password for a mailserver. For unknown reasons (until now) sooner or later the behavior would self-correct and the password requests would cease.
Seems I've tracked this down. One of my current email providers has a hard-limit of 50 simultaneous requests per IP address. I have 4 email accounts on that server. This *always* fails. In their IMAP server log files they see:
May 4 11:06:33 server308 dovecot: imap-login: Maximum number of connections from user+IP exceeded (mail_max_userip_connections): user=<firstname.lastname@example.org>, method=PLAIN, rip=188.8.131.52, lip=184.108.40.206, TLS
So even though my mail check interval is set to 5 minutes, the server is seeing 50+ IMAP connections.
I have configured the same email account in Thunderbird, and even set the update interval to 1 minute, and I do not hit the max connections.
Anyone have any idea why Mail.app would be trying to make 50+ connections? Or simply not closing the connections it opened previously?