This morning I woke up and noticed that the house was unusually cold, and it wasn't warming up as quickly as usual. As I walked over to my Nest thermostat to check it, I noticed the green light flash and when the display turned on there was a message saying "Delayed for m:ss," where m:ss was counting down from two minutes and some seconds. Oh, joy, another issue with my HVAC system! :(
(My previous issue was a clogged drain from the natural gas heater, which tripped a safety and shut down my heater during the first cold snap after I moved in. Fortunately the builder got the HVAC contractor out the same day to fix it.)
A quick search of the web turned up the solution: unplug the Y1 wire during the winter. Y1 controls the air conditioner, and apparently this connection can drop the voltage enough when you don't have a C ("common") wire that it creates an error condition in the Nest and the heat won't stay on.
This reminded me of a conversation I had with the HVAC contractor when he came out to fix the heater the first time. He noticed that I had a Nest and he initially thought that the problem might be the Nest's lack of a C wire. He'd had several other customers whose Nests weren't working well until they installed a C wire, and he suggested that he could pull a new cable from the furnace to the thermostat with another strand for the C wire. (Unfortunately my current cable only has four wires, all of which are used; I need a new cable with a fifth wire for the C wire.)
While unplugging the Y1 wire is a pretty quick and easy work-around, I'll probably end up having the HVAC guy run a new cable come spring when I need the air conditioning again.