Hi, I understand why this is frustrating. A paid Microsoft 365 subscription doesn’t guarantee permanent sign-in; Microsoft may still request identity verification for security. However, that doesn’t establish why both accounts are being signed out every month.
Are you both using the Outlook app on Windows, or accessing email through a web browser? What exactly does the sign-in message say?
If you use a browser, check whether it or a cleanup tool automatically deletes cookies. Deleting cookies can remove your saved sign-in session.