Using classic Outlook for Windows in business environments
Me and the wife are having the same issue.
I use BlackBerry Hub on Android, started prompting at the start of the week. Managed to get it going using different server URLs for a short time, e.g. outlook.com, outlook.office365.com, hotmail.com, microsoft.com with varying degrees of success. Outlook.live.com seemed to work for a few hours then got the same error.
Wife just uses native iOS mail client and is also prompted for password.
Utter shambles, considering moving away from Microsoft for mail. Wasn't keen on Google but at least I wasn't stuck without mail on my phone for a week.