Using older versions of Outlook for Mac for personal email and calendar
Finally solved this with the help of my IT department (they are amazing). Here's what they told me to do:
You need to update the desktop app on the computer. Running 16.55. It is at 16.65 now. Go to Macintosh HD > Library > Application Support > Microsoft > MAU2.0 > Microsoft Auto Update.app
That explains why it stops working occasionally.