In this case are you saying that there is a password prompt for the users credentials? Clear the Windows Credential manager or recreate the users Outlook profile. In fact if you just turned on MFA and you were not using MFA before you usually end up having to rebuild the profile and clearing the credential manager. If you are saying that they are getting multiple MFA prompts then this is an out of sync issue with the wrong code being used.

Additional resources

Please help can't afford a new computer if I throw this one against the wall. Yeap, you describe it exactly and unfortunately we still don’t have an answer. Closed the window without entering anything and Outlook returned to ‘Connected to Exchange’. Office 2016 is already Modern Authentication aware so APP passwords are not required.

Microsoft Office 365 Endless Authentication Loop Issue

• I wonder if the compuer cached a new logon token or something that the old Outlook profile could use.
• I experience the issue myself as well, every once in a while.
• In each case the fix has either been one of the above items or a combination of them.
• I then approve the login with my authenticator app.
• Outlook must be online or connected to complete this action.
• Those versions have been updated to prevent the problem that is described in the "Symptoms" section.
• If you are saying that they are getting multiple MFA prompts then this is an out of sync issue with the wrong code being used.

You may have to rebuild/restore your outlook folder/files which is a pain. I’d do that one step at a Outlook profile repair and recovery steps time, forgoing the restore of the cached files. If this box is greyed out or disabled then you need to reset the Windows Credential Manager first. Or, any suggestion on how to fix this issue, even better.

Outlook stuck in an MFA loop

Close and open your web browser again and go into Troubleshoot Office 365 Sync and Login Issues SuiteFiles. You will most likely need to enter your Microsoft 365 credentials again so ensure you tick any box that says remember my credentials but it should now work for all future documents you open and not require your credentials. Upgrade to Microsoft Edge to take advantage of the latest features, security updates, and technical support. I regret that you are experiencing issues with your Microsoft installation.

Outlook 365 Password Prompt Issue on Windows Desktop

So not doing anything at all even seems to work. Which to me sounds credential loop in Microsoft 365 like the issue is service side, not client side. Problem doesn’t just happen on PC’s connected to the internal network, but can happen when a laptop is remote and connected via external wifi or mobile hotspot.