Central Heat Won't Turn On When I Raise the Temperature on Nest Thermostat
Is this a heat pump?  It sounds like a heat pump.  

To quote Boromir, "one does not simply cycle a heat pump on and off."  Heat pumps are similar to air conditioning units (but with the ability to pump the other way).  When they shut off, they need some time to stabilize before they start up again, otherwise you have what's called a "short cycle" which can damage it.
Most units have an internal protective circuit to make sure it doesn't restart too soon after a shutoff. 

If you command increased heat shortly after it has shut off, the thermostat might call for heat, but the internal protective circuit will prevent it from starting right away.  This may cause the thermostat to call for 2nd stage heat.