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I experience the issue myself as well, every once in a while. Tried CC cleaner to clean up registry and everything -- also keep in mind this FixTechGuide Office 365 troubleshooting is a fairly recent reinstall of windows. I am unable to stay signed in to my work account on Teams, Outlook, Office365 for more than 5 minutes.
Outlook credential prompt loop
I disabled the Zoom and Adobe PDF plugins and it stopped prompting me immediately. My client’s Outlook will only continuously ask for the password Repair Outlook Profile Online after MFA is enforced and Office.com has been logged in. It would be nice if it distinguished between your password and the app password. You may have to rebuild/restore your outlook folder/files which is a pain. I’d do that one step at a time, forgoing the restore of the cached files. Not sure if it has to do with being an onmicrosoft.com account that has no domain assigned to it.

Loop of 'Sign in to your account'.
I had this exact issue on another machine, that after 2.5 hours on the phone with MS support (via Zoom), the solution was to uninstall MS Office 365 and reinstall it. 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’. I created a new Outlook profile, and then the old one started working. I wonder if the compuer cached a new logon token or something that the old Outlook profile could use. Also, during the new profile creation, I was only prompted for a password and not for MFA.

Resetting the Windows Credential Manager:
When we opened the old, existing profile it didn’t ask for ANY authentication, it just started working. Office 2016 is already Modern Authentication aware so APP passwords are not required. Native IOS and Android Mail apps will require the APP password or users can use Outlook for IOS/Android which is Modern Auth aware. FYI outlook 2013 requires a registry setting to work with MA. Where I work, we have a new sandbox tenant to make tests before clear Outlook credentials manager official deployment. I tried registering the account to my Outlook Desktop app and for some reason I am in a credential prompt loop that always asks for it anytime I input my password.
- If this box is greyed out or disabled then you need to reset the Windows Credential Manager first.
- Out of 140 staff the problem seems to occur once every 2-3 weeks on average.
- But by mistake, I turned on MFA for the admin account, and then when I logged in again, it prompted me to use Microsoft Authenticator.
- I experience the issue myself as well, every once in a while.
Changing Outlook Security Settings:
If this box is greyed out or disabled then you need to reset the Windows Credential Manager first. @Microsoft, given the level of attention the community has given this issue, I hope you come up with an update soon. We have been experiencing the exact same issue for months now.