OUTLOOK - Continually Requesting Password

There are many answers to this issue as a quick Google search will show you. For my particular configuration of Outlook, Exchange Server 2013, and Office 365 there was no solution readily available so I had to work through it and thought I'd post the solution here.

ISSUE: Outlook continuously requesting a password. Sometimes it presents an anonymous sign in box (by anonymous I mean that you can't really tell which account wants the password). You can close, (X), the password request box and Outlook continues working.

SETUP: Outlook on desktop, accessing an email account on Exchange Server 2013, Office desktop Apps installed from an Office 365 account.

SOLUTION: In Outlook, click on the 'File' tab and select Office Account. Sign out from the Account, (underlined in red in the image below). That's usually enough to silence the password requests.

For a longer term solution, sign back in to the account with a valid Office 365 Account, and then sign in to any additional password boxes that pop up with the same Office 365 Account details, change the sign in account if you have to. In my case the password boxes displayed the Exchange Account and what was actually required was the Office 365 Account.