The weird thing is that this happens to both remotes at the same exact
times and days of the year. In another hour, they will both be fine,
and the episode won't repeat for another two weeks to a month.

It could be a temperature/condensation effect, perhaps. If an
electronic device is left in a cold room, and then exposed to warmer
and moister air, moisture can condense on the internal electronics and
create low-level current leaks which can cause a malfunction.
Sensitive scientific instruments "brought in from the cold" sometimes
need to be kept in a sealed container until they warm up to room
temperature, for this reason. Years ago I had a "haunted" Macintosh
II which would power itself up in the morning for no obvious
reason... condensation hitting the "power on" contacts in the keyboard
were responsible.

The other possibility is that you have some device in the room which
is emitting enough pulsed IR to "jam" the IR remote sensor in the
television... it might not see a key-press, or might see a key-press
and then not the key-release signal (and so would "run away" with the
volume going all the way up or down).

Compact fluorescent lights, or other fluorescent lights with
electronic ballasts, are notorious for causing IR-remote problems.
They "flicker" at a rate of 40 kHz or so, and can saturate the IR
sensor in a television. It's possible that you have one of these
whose pulse rate occasionally drifts into the TV's IR passband and
blocks signals from your remote.

If you're using one of those horrid X-10 "IR over RF" repeaters (the
black pyramid type)... these, too, are very subject to jamming
problems. Even having one of the receivers in the same room as your
TV can cause problems - if it picks up random RF signals it can
transmit them as IR and confuse the TV.