Why would my Maytag FG6RC high efficiency furnace restart in the middle of a heating cycle?

My furnace is probably 7-8 years old, and this heating season the furnace has developed a strange problem. The furnace starts normally, but before the temperature reaches the thermostat setting the gas valve shut off. The main blower continues to run for a short period, than shuts off as normal, but the exhaust fan continues to run. After about 20-40 seconds the heating process start over again. The gas valve reopens, and the furnace restarts.

During these cycles the yellow light on the thermostat is still on, which is normal when the heating cycle is active. I’ve tried raising the thermostat temperature setting by 10+ degrees to rule out an issue with the sensitivity of the thermostat. I live in Michigan, and over the past several weeks our high temperature have been around 10-14 degrees. The lows at night have reach -17 degrees, so the furnace is getting a workout.

Any information you could provide as to the issue I am having would be appreciated.