My best guess right now is that there was sufficient corrosion on the battery
terminals that the battery
went for a good long while without getting charged. It didn't show up because while plugged into shore power, the trailer's little panel voltmeter was reading voltage from the charger (13.7 volts), and when I had the trailer plugged into the tow vehicle, the running lights
and turn signals all worked (duh!), so no difficulty was noted until arriving at the campsite with no shore power, disconnecting the tow vehicle, and then we found the house battery
totally flat. Jiggling wires during the preliminary WTF??!? investigation restored the circuit enough to allow the TV to charge the battery and we were operational enough.
I must not have checked the house battery voltage at home after disconnecting the shore power just before hitting the road. I think I left it connected until the very last minute so that the fridge
would keep working. (Hot day!)
I would call the corrosion on the battery terminals very minimal, so I'm surprised that it stopped the charge and caused the battery to be totally flat. But looking back thru my log, it's been at least since May that we were at a campground without electricity, so the battery may not have been topped off for quite some time. Plugged in at home, and plugged in at a campground may have lulled me to sleep WRT to the status of the battery.
This all suggests a much more diligent monitoring of the state of the battery charging process. I think I might also solder the battery connections (in stead of the cheap crimps that are original).
Is there a way to monitor the state of the battery charge while it is still on the charger? I bet it takes a smarter charger than the Progressive Dynamics one that also was installed when new.
Thanks for helping me think through all this!