Hi!

Could it maybe be that the fridge in question was working,
just not frequently enough to keep the freezer compartment
cold enough?

I think that's a very good suggestion, and it certainly could make
sense. This refrigerator is a "grown up" version of something like a
dorm fridge, and the only thermostat it has is in the refrigerator
portion. Cooling is accomplished by a "pad" mounted in the bottom of
the freezer with refrigerant running through it. A similar method is
employed in the refrigeration compartment, where the pad is located in
the rear of the unit.

I'm still wondering about why it is that old refrigerators will work
where new ones do not. I've seen a lot of old fridges in unheated
garages that work perfectly no matter the temperature--units made in
the late 40s all the way to the early 80s. There's not a lot of
obvious difference in the later ones compared to brand new units--both
usually have a fan and the majority of cooling functionality centered
in the freezer where a damper directs some air off to the fridge. The
actual working thermostat is in the refrigerator portion.

One other unrelated thing to check is that the defrost mechanism
is working properly.

There isn't any defroster in this particular unit. It has to be done
manually for the freezer. In the refrigeration section, the coil can
drain into a pan on top of the compressor.

I am thinking about obtaining a very low current "thermostat warmer"
device and mounting it in the fridge near the thermostat. When it's
very cold, I could energize it every so often on a timer to force the
refrigeration system to run.

William