I had a problem with mine once, and it turned out to be the crappy push
in terminals on the switch. Replacement models have both the crappy
push in terminals and regular screw terminals (like the back of an
electrical outlet).

I had the same problem or similar. The push in connectors were
different on the new switch compared to the original.The furnaces
wiring would go into the push in connector but didn't appear to be
very secure, so I soldered on larger gauge pigtails to the original
wiring. I then plugged the proper sized wire into the connectors.

I wonder if his connectors are arcing and failing?