Ok, finally have a resolution, sort of. As a starting point after receiving your input was to first get the batteries charged. As pointed out above, it would be damaging to the batteries to let them sit with very low voltage.
So, with no other changes, I put an external charger on the batteries. They charged fine. Next I removed the external charger and put the RV back on shore power (in storage). The batteries showed to be maintaining on shore power so on a whim I left them there, on shore power charging to see what would happen . . . they stayed charged.
Next I took the RV off shore power. The batteries began to lose charge, but at the expected very slow rate. When the batteries reached low 11 volts, I reconnected shore power.
They Charged!
The problem hasn't been solved, but it has gone away.
I don't plan to test it, but I suspect something in the system, from the converter to the batteries, is inoperative when the batteries reach a very low voltage. To avoid the problem in the future, I just need to keep the batteries well charged.
Time will tell.
Thanks for everyone's input.