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.)
Learn how to sign in and create app passwords for Microsoft apps and devices that don't support two-step verification.
support.microsoft.com
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)
Learn more about the POP, IMAP, and SMTP settings for Outlook
support.microsoft.com
So far I have been using this for the last three weeks without outlook asking me for the password.