Most self-igniting gas furnaces must have a grounding system for the circuit board to recognize the flame. The flame is recognized by alternating current (wall plug) traveling across the natural gas flames and converting to pulsating direct current (battery) terminating in the chassis of the furnace. If the furnace is not properly grounded the voltage will not travel across the current because it is an open circuit. It would be like plugging in only one wire of your vacuum cleaner into your wall socket and expecting your vacuum cleaner to work. The furnace circuit board is usually grounded through one of the attaching screws.
If you have a bad or open neutral leg going to the furnace the 120v power cannot complete it’s circuit and the power leg for the furnace shuts down. Poor contacts usually let the furnace turn on, but when the blower motor turns on the amperage draw (amount of electricity used) increases and this causes a voltage drop. It is often a significant enough voltage drop to cause the circuit board to think that the flame has gone out. The circuit board reacts by switching the gas off.
This is usually just a maintenance issue. If the spark rod (not all furnaces have these) becomes corroded or dirty the electricity traveling through the natural gas flame cannot connect or pass through the rod. This lets the circuit board know that there is no flame present and the furnace circuit board will shut the gas valve down. The spark rod is a ceramic encased piece of metal. The ceramic portion is held onto to the burners via a clamp and the exposed metal portion is actually in the burner flames. If the metal is grounded due to a cracked ceramic base the spark rod will not transmit the pulsating DC current to the circuit board and the flames shut down.
This is common problem. A worn or cracked (not always visible to the naked eye) hot surface igniter has too much resistance to electrical flow and does not allow enough electricity to travel through it for the flame rectification circuit (A/C to D/C power transformation). Hot surfaces igniters typically still light the gas flames when they are cracked.
If the flames does not fully engulf the hot surface igniter or the spark rod it can move away from them. If this happens even for an instant the circuit board will shut down. This can be caused by an inadequate gas supply from water and debris in the piping, gas valve not turned on all the way, to small a gas line, rust covering the burners and spider webs in the burners.
Defective high limit control or flames that are too high or too close to the position of the high limit control. This can be caused by excessive gas pressure, air fuel mixture not adjusted properly or a defective gas valve.
Debris in the fan blower wheel, birds nest, roofing materials, water and rust can reduce the airflow enough that the air switch drops out of the circuit and tells the circuit board that the vent is not working.
A collapsed cap, disconnected piece of venting in the attic or a deterioration of the inner liner of a dual wall vent pipe (vent piping in the wall or attic is dual wall for residential forced air heaters below 90% AFUE) can cause a reduction in vent airflow and this results in the air switch dropping out of the circuit and the system shutting down. Often the furnace starts and the expanded characteristics of the hot vent gases overwhelms a problem or poor vent.