Nevermind -
After digging into the activity logs as suggested, I discovered that there was a suspicious entry relating to the private endpoint connection proxy getting overwritten.
Apparently someone was attempting to create an additional extraneous private endpoint for the same resource, creating a conflict. It seems that when that happens "Azure Traffic Manager and DNS" doesn't recover well; even though the extraneous private endpoint did not persist and ended up getting removed again, the change of the private endpoint connection proxy due to the attempted configuration of the extra PE seems to have caused "Azure Traffic Manager and DNS" to remove the "incorrect" A record. But then it did not replace it with anything
This is my best effort to understand the situation at the moment. I may not have explained it 100% correctly, but this is how it looks based on the logs I've seen.
My focus is going to now be on helping explain to this user why the second PE is not required, to avoid attempting to create that, and then resolve the separate networking issue that was prompting them to do this in the first place.