The domain is correct, and that wouldn't explain why it stopped working out of the blue or why it keeps asking to type the password and it doesn't send the mail.
Some suggestions/thoughts
1. Sometimes email accounts get buggy, it even happens with google apps, if there is no email stored in the actual account then perhaps delete the account and recreate it. Alternately you can create an alias for that account and then delete the main address and then add the main original address as an alias and remove the temp alias. (if the mail server supports this)
2. There may be some bot trying to break into his account with a brute force and that can be causing him issues with his login, this was happening with my yahoo account there was a bot/hacker in Poland trying to break into my account and my phone kept popping up with password errors because of that. When i turned on 2step it magically stopped. I would suggest turning on 2 step temporarily until it stops.