Thank you for all the advice. It is an old Honeywell manual thermostat.
Indeed there is power to the furnace, with a switch box. The furnace
was installed 1992. I have watched the burner sequence many times. The
thermostat is indeed calling for heat as it should. The ignition is
firing red hot, but it doesn't appear to be getting gas for those
several hours. This is what made me think it was a gas pressure problem
upstairs at peak hours (when people are at home in the evening), but
that may be ignorance on my part. I have looked all over for the timing
mechanism that could explain the problem but can't find it. There is no
wiring that would explain it.
I'm beginning to like the ghost explanation. Anyway, my wife is pulling
her hair out. And you can imagine what no heat at bedtime is doing for
the more personal aspects of my life. Argh.