Mail won't send from non-Mac servers. Restart mail, it's OK.

Every since "up"grading to Mountain Lion, two or three times a day, Mail will return errors for all my non-Mac (gmail, Exchange) accounts when I try to send Mail, and it takes all my non-Mac (gmail, Exchange) accounts offline, and offers me the me.com/mac.com/cloud.com server for sending messages. Reentering passwords does nothing. Reconfiguring accounts does nothing. Force quitting Mail and restarting fixes it. Grrr.