Mail

Safe Boot from the HD, (holding Shift key down at startup), does the problem occur in Safe Mode?

Safe mode attempts to repair Disks & clears lots of caches, so if Safe Mode works try again in regular boot.

If still no good Disconnect from the Internet, then start Mail, look for the last rec'd eMail.

Quit Mail & login to your WebMail in a Browser, if possible delete any later eMails there after the last rec'd one on the Mac.

I had the same thing happen to me, in Catalina in this case. I disabled accounts one by one in Internet Accounts until I found which one seemed to be causing the issue. It was an Exchange account. I deleted the account, then added it as a new one, and, so far fingers crossed knock on wood and all that, Mail is staying open. There's no telling for sure what caused the issue, unfortunately, but for now this seems to have fixed it.

Good work, thanks for the report back. :)

Good work, thanks for the tip. :)