Mail.app has stopped accessing several of my gmail accounts. It gives the generic error "Mail can't connect to the account "xxxx". Enter the password for user "myusernamehere". When I enter the correct password, it circles back to this error. Going directly to gmail, I can login with that same password.
One of the two accounts with this problem is a new one I was setting up, but the other is my "main" account which has been in use with mail.app for years.