Exchange Password Required notification repeatedly keeps popping up!

When I see " Apple, PLEASE fix this issue as it makes MAC OS unusable! "

Apple is not here and will never respond to this request

These Forums are only fellow user like yourself and me

Then have a few suggestions ;

1 - Get Support Choose a product and we’ll find you the best solution.Start now and open an Apple Support Ticket as they are Apple Employees to deal will these types of issues . 

2 - Product Feedback - Apple and make it known to Apple regarding this ongoing issue 

Building on Previous Contributors' posting.

Much like Apple Requires Application Specific Passwords when using Third Party e-mail Clients to access iCloud e-mail Account.

Perhaps a similar requirement is needed when using Apple Mal to access Exchange e-mail Servers

refer to Apple Support Documentation

link below

Sign in to apps with your Apple ID using app-specific passwords - Apple Support

Apple can’t do anything about your Exchange server password.

There was a bulletin from Microsoft a while back warning users that they were going to start requiring two-factor authentication. Perhaps this is what you are seeing? I haven’t seen any changes on my accounts yet.

Instead of responding to the pop up, have you tried going to System Preferences Internet Accounts and entering the password there?

Are you using Apple Mail or Outlook? With Outlook, when you enter the password you are asked if the password should be saved in the Keychain, and you should answer yes.

Apple’s OS can, and does control notifications from other apps and it can for this app. My password is not related to the continued, uncontrolled notifications allowed from the OS, especially when the account is marked inactive.

All my accounts have two-factor authentication enabled as well.