Central heat doesn't always kick back on
Your thermostat turns the furnace on and off. Off is easy :-) But sometimes when it turns back on, something doesn't work quite right. It could be a sensor that detects a temperature too high, a sensor that is supposed to detect ignition that doesn't (either due to a sensor problem or because the burner really isn't igniting) or something else. When that happens, the furnace stops trying, because (essentially) it has decided that doing the same thing over and over again will not produce different results. So it is now &quot;locked&quot; in a mode where until something changes it will not try again.
Then you lower the temperature on the thermostat. That tells the furnace &quot;I'm warm again, you can stop trying.&quot; It then turns off certain key circuits. When you raise the thermostat temperature again to call for heat, the furnace gives it the old college try and this time it works!
This is not that unusual. It actually could be worse - I had a problem a few months ago where the thermostat trick wasn't enough and I had to cut all power to the furnace - and then it started working again.
If it happens once a month, you can probably ignore it. If it happens every day, get it serviced. The problem may be as simple as too much dust in the wrong places, but it could be a sign of real problems and a possible safety issue.
Safety Reminder - Carbon Monoxide
As my HVAC tech made sure I did the last time I had a big problem with my furnace, anyone with a gas furnace should make sure to have Carbon Monoxide Detectors in the house. Not right next to the furnace (too much of a chance for false positives) but definitely not too far away as the danger is very real - and impossible to detect with your nose. Incomplete combustion can cause a furnace to not always start correctly, and can also lead to deadly levels of carbon monoxide.