In the past couple of weeks, I've opened my Outlook that is configured for my GoDaddy email account (associated with a domain) and been asked to supply the Microsoft name/password. Sometimes it takes and sometimes it doesn't and I have to wait. I called support and was asked TWICE to change passwords. I'm tired of doing this.
See you've yet to receive a response...
Do you have any ad-blocking or privacy software in place? Sound like cookies are possibly not being saved.
Try adding the URL for the login you are having issues to your approved sites in your browser and see if that makes a difference.