>I have a situation into which Outlook, randomly, keeps asking for credentials about one of my accounts. I use Exchange Online. I have several accounts and two of them are using Exchange Online. One of them never complains. The other one shows the login screen occasionnaly. If I ignore that, I can send and receive emails for that account. If I enter my login information, a few minutes later, it starts doing that again.

The credential management Outlook has always been a roll of the dice.
With version 2016, the thing is improved.