Using New Outlook on Windows for academic communication and scheduling
I have a slight workaround I use in Chrome which works if you're on desktop and your organization is using 365. I have a tab open which is logged into the main "Home | Microsoft 365" Dashboard where you can get into Outlook and your calendar and organizational stuff, I don't really use this much but...I have a second tab open which is specifically my Outlook web mailbox.
So now, the Outlook 365 dashboard tab is the one getting logged out and not my mailbox. My inbox continues to work as usual and I don't care if I ever log back into the dashboard tab.
I have been using it this way for about 2+ weeks without fail, email never logs out. My issues started 3-4 weeks ago when most other people started experiencing it.
Good luck if you're on phone or something.
TL;DR:
Tab 1 - Microsoft 365 Dashboard becomes log out target
Tab 2 - Outlook Mail tab business as usual, never logs out