Air filters that are clogged with dust and dirt can cause this problem. Today's furnaces measure air flow speed through the furnace, and if a clogged air filter is preventing proper air flow, the furnace will shut off within minutes of starting. That is an inexpensive fix you can do yourself. One other issue could also be a cracked or corroded heat exchanger. If the heat exchanger is cracked, it may be allowing the flame from your gas furnace to back up into the furnace. There is a sensor called a 'spill switch' that will detect the flame and shut the furnace down. If changing the air filter doesn't seem to fix the problem, call for service. In the Little Rock, AR area Ski Brothers Heating and Cooling provides central heating and cooling, air conditioning service, and heating and ac service everyday. We are open Monday through Friday, 8 to 5 PM. We have great reviews, and will come to your rescue quickly!