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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. The bad thing is this account was not registered with Microsoft Authenticator, so I couldn't see any codes online Outlook email repair utility in the authenticator. And there were no other login options, and I was stuck in a login loop. This is now the 2nd machine that presents the same issue. I have a valid MS 365 subscription that includes 5 device licenses. On the main machine where I have been using the suite, now my account is deactivated and if I try to authenticate, it looks like it works but then get the "Fix", "Authenticate", "Activate" or "Resolve" buttons, all of which do nothing.
Outlook credential prompt loop
In the instances that this occurs the effected user is not new to MFA but has been running it for at least months. The problem appears to randomly affect users (I’ve had it affect myself once too), and the only solution appears to one of (or a combination of) the options in the OP. Out of 140 staff the problem seems to occur once every 2-3 weeks on average. 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 resolve Outlook not sending emails fast the profile and clearing the credential manager.

Loop of 'Sign in to your account'.
We had the issue where Outlook 2016 kept prompting for a password for an Office 365 user whose laptop was connected to their Office 365 account using Windows 10 Pro. The repeated issue logging in started after I enabled the modern authentication in the Office 365 administration panel. The user could use the Windows mail and calendar apps but Outlook wouldn’t connect and kept prompting for a password. Checking the Account in Word showed the correct authentication and subscription.

Resetting the Windows 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. We’ve got a support case opened with Microsoft on this one but it’s been rebuild Outlook data file quickly open for about 3 months. Unfortunately when the problem occurs they’ve asked us to ring straight away but of course you can never get them instantly (we’ve just been given someone’s direct number now). To make a long story short we’ve since been asked to collect Outlook logs and install Fiddler to capture additional logging. Initially, this account didn't have MFA turned on, and I was able to log in.
- If this box is greyed out or disabled then you need to reset the Windows Credential Manager first.
- I created a new Outlook profile, and then the old one started working.
- 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 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.
- I'm also getting Error 29, which the MS support rep couldn't explain to me.
- I experience the issue myself as well, every once in a while.
- I’ve seen this happen when the time and or date is wrong on the machine.
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.