I didn't notice until late in the afternoon, but according to the Apache logs, around 3AM this morning the server shut itself off (probably suddenly or violently).
When I was finally able to get to the server (about 6:30PM), I quickly determined that there was a power supply failure; no obvious electronics failure, and the PSU wouldn't even flicker with a tap of the power button. Toggling the PSU power switch and even plugging it into a different cord didn't matter, either.
I was able to jet to the parts shop and get a new PSU installed by around 9PM. A few starts with the case open, one false start as closing the case unplugged the boot drive power, and another false start as it seems the CPU fan was knocked loose, and all was well again.
There were two "failed" servers, as the unexpected shutdown left "lock" files behind, but removing those allowed the apps to recover, and now all seems well again. There's e-mail flowing, and the logs show that web traffic is again flying from the machine.
Apologies if you were affected.