I’ve had the same issue with both my Nest E. It would cycle on and off
and stop working eventually after a few cycles. I replaced one nest E
with the old dumb thermostat. That did not work. After replacing both
thermostats, everything is back to norm...
Same issue here. Eventually in the mornings after a few of these short
cycles, I have to flip the breaker to the furnace to work again. I also
did a hard factory reset. Before the reset, the furnace would not come
on at all.