The settings on the SQL Server Agent Properties, History, were the problem. Apparently someone (or something?) else had been changing them after I checked them. I don't have...

No, there are no cleanup jobs or cleanup maintenance plans that I can find

nekonecny,

I don't want to purge job history. I am trying to determine why the history is disappearing before coming anywhere near the limits I have set.

No, I did not.

George,

You're right!

For some reason, the first time I tried to offline it, that process just hung, and wouldn't even come back with an error except to say it timed out,...

Finally -- success!

Thanks to Steve Jones. He wrote me "What about detach, rename log, attach with rebuild?"

So, I researched this for a few minutes, having not heard of it.

Then,...