But THAT was the problem. Half the groups it listed me as belonging to are NOT groups I belong to or ever have.? I checked the error message my server sent and the bounce was triggered by a single message from a group I DO belong to which stated it had tried to reach an address that didn't exist. There was no threshold of multtiple bounces that was exceeded.
?
Fortunately, it appears to have been part of the general issue with Google that happened today. Messages received by GMail from the groups were bounced back as "no such address".