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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 Microsoft Outlook Email Repair Tool Online 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
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 diagnose Office activation conflicts 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:
I have contacted my organization and everything looks alright from their end.. I went as far as getting a new device but it did not cut it. When I try to sign again it will be stuck in sign in loop with the message " Taking you to your organization sign in page" after I have logged in on my company site... When I log in to my account at first from a new device or after a while, it stays signed in and I can work peacefully for about an hour, then it automatically signs me out. Or, any suggestion on how to fix this issue, even guide to Office 365 sign-in errors better. I do NOT have this issue with the other laptop, an iPad, a MacBook Pro and tablet.
- I even tried disabling my anti -virus while authenticating, that didn't work.
- Right now we have it set to prompt when a user is not on any of our corporate networks or they are using a mobile device.
- I cannot find the phone number again to contact MS Office support (eventually they were helpful, but only after insisting they help!), I'm in the Netherlands so if someone has a phone number, I'd love to get it again.
- Where I work, we have a new sandbox tenant to make tests before official deployment.
- I do NOT have this issue with the other laptop, an iPad, a MacBook Pro and tablet.
- 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.
Changing Outlook Security Settings:
Hi, my office 365 account used to work with my desktop apps, I have confirmed with my admin system twice already that I have the appropriate license and everything is enabled but i keep getting stuck in this loop. We are looking at using conditional access policies where a user with a Domain joined PC is not prompted for MFA. Right now we have it set to prompt when a user is not on any of our corporate networks or they are using a mobile device. The user had Office 2015 and Office 2016 credentials and Teams credentials that we deleted. We checked with Word that the account was connected–it was and the we opened Outlook and it immediately connected. We too have been seeing this more and more, all W10 on O365, although we use Okta as our MFA.