It very well may be over temping and shutting down. If the exhaust is not restricted then try this. Heat may be building in the blower area because there are not enough discharge ducts installed to move the proper volume of air thus allowing an over temp condition.
This is fairly easy to correct by getting the necessary parts and installing another duct. Usually a short run that allows more air out of the furnace into the living area. The furnace may have to be removed so a duct blank can be removed and the ducting adapter installed. Install a register for the outlet and connect up with the duct tubing from the furnace.