I've found many threads similar to our problem, but none that seem exactly the same.
Several of my Exchange users are prompted for passwords by Outlook while it is running. If they cancel, Outlook goes offline with "Password Required." If you click it, Outlook reconnects. If you try and enter network credentials, they are rejected.
This began after I migrated users from O365 to on-premise Exchange. I've created new Outlook profiles and not all users have this issue. We still use O365 for FOPE. I have a suspicion that the credentials prompt is not for Exchange but for O365. I cannot confirm, but I believe that it may be users whose passwords did not match as ADSync wasn't pushing passwords.
I would like to get these users back to normal. I wiped Office from someone's computer completely, deleted registry and folders, rebooted, reinstalled and the same problem occurred.
Any advice is greatly appreciated.