The short and curlies.
ENSURE YOU HAVE THE CORRECT LOGIN DETAILS AND PASSWORDS PRIOR TO THIS FIX. IF UNSURE ASK AND CONFIRM BY LOGGING INTO YOUR EXCHANGE WEB PORTAL.
Close Outlook 2013 / 2016 / 365.
Open Control panel and go to Mail Setup Outllook / then open Email Accounts
Delete the account which causing the issue. (dont worry if its exchange you will not lose any mail items, they will be re-populated once up and running)
Open Computer User Credentials Manager. ( Click on start and then your Login Picture and select - Manage Your Credentials. ) ( Control Panel - Credentials Manager )
Expand and Delete any credentials pertaining to the account in question. BOTH in the Windows Credentials and Generic Credentials. If there are more than one delete them all if they are for the email account you are experiencing the issue for.
Go back to Control Panel and open Mail Setup and select "Setup email accounts and directories"
Setup your email account as you normally do. type the password when prompted and complete.
close out when finished, open Outlook and see.
The password prompt should not be annoying you any longer.
Note this will only work if you have the correct password or else it was a waste of time. Confirm your password by logging into the exchange portal of your domain if unsure.
Hope it works for you as it has for me on many occasssions...