I have been having this exact problem like everyone in this thread.
Outlook is prompting for the Username/Password randomly when Outlook is open.
Trying the Username/Password combo finally works after about 5 attempts or so,.
The Username/Password will then come up again randomly afterwards. 5 attempts or so and it lets you into the mailbox.
While waiting for a Microsoft fix (hopefully), I tried those server names:
imap-mail.live.com
smtp-mail.live.com
Without the actual SSL ports listed, I was not able to connect to these using TLS or SSL on port 993 (imap) and 587 (smtp).
Either way, any updates are appreciated if they come around,