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Same issue here, getting prompted for the password. And, that's even if I reenter my password.
My Outlook.com account is added as Outlook.com. Maybe I will try it as Exchange.

EDIT:
Tried to add my Outlook.com account, as an Exchange account. But, I do not know all the server information, and such. Time to Google it - LOL
Apple has a web page showing all relevant Settings/Info for all the major email available
 
I'm telling you folks, this is not a new issue. it's been around since IOS 13 or earlier. It's an Outlook/Microsoft issue. No pattern or reason to it. Appears and disappears just like your friendly ghost. You all do a google search and you will find a vast number going back at least 4 years on this Outlook issue. It's not just IOS mail client, but eMclient, outlook and others. Temporary fixes only.
you maybe correct as I do recall being prompted in the past (I think)
 
Setup via Exchange does not work for me, with my Outlook.com account.

Over the past few days, I had to reenter my Outlook.com password at least once a day. Even this morning, I woke up and thought it strange that I had no new email notifications. Around 10:00 or so, I opened the email app, and was asked to enter the password...
 
There was a partial outage! This all happened as I’d bought a game online and the code was sent to my outlook email! I was really angry lol
 
This issue predates IOS 14. Goes back as long as I've had an Outlook mail account. It also happens on my PC and has occurred for a number of years with Windows Mail, Outlook Mail, EM Client as well as others.
It is something I’ve experienced from time to time over the years too. I think the difference is that it now “seems” to be Microsoft only and can happen several times a day
 
I had that issue with the default iOS mail app asking for password recently. for outlook every few days.

What I did was remove the outlook account from the mail app. Then setup app password in your outlook account. (If you try to use the app password in outlook.com when adding to the default mail app instead of other. It doesn’t want to accept the app password.)


Go to the Settings - Mail - Add Account. (Do not select outlook.com). Select Add Other - Add Mail Account

Here the link for the settings you need to manually add. (Look for the outlook.com settings imap and smtp)



So far I have been using this for the last three weeks without outlook asking me for the password.
 
I had that issue with the default iOS mail app asking for password recently. for outlook every few days.

What I did was remove the outlook account from the mail app. Then setup app password in your outlook account. (If you try to use the app password in outlook.com when adding to the default mail app instead of other. It doesn’t want to accept the app password.)


Go to the Settings - Mail - Add Account. (Do not select outlook.com). Select Add Other - Add Mail Account

Here the link for the settings you need to manually add. (Look for the outlook.com settings imap and smtp)



So far I have been using this for the last three weeks without outlook asking me for the password.
It’ll come back. Been happening without an established pattern for couple years.
 
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