The Password rejection can confuse people since it's a catch all meaning...
This Password, Username, Authentication method... is not recognized on this Port to this Server, or a server end problem.
If using a browser to login via WebMail works it's not Name or Password, but one of the other ones.
The receiving email ports are:
IMAP is port 143
IMAP-SSL is port 993
POP is port 110
POP-SSL is port 995
Outgoing ports are...
SMTP and SMTP-SSL is on ports 25, 587 and 465. Port 587 has to be SSL, and port 465 is enforced TLS-wrapped and is generally used by Outlook users.
Open Keychain Access in Utilities, use Keychain First Aid under the Keychain Menu item, then either check the Password under that item, change it, or delete it and start over. There should be 2 entries for any email addy… in & out.
This happens to me periodicaly. If I simply dismiss the popup by hitting Cancel and then Get Mail from the affected account, it works right away.