There could be several reasons why your furnace won't stay running, such as a clogged air filter, a malfunctioning thermostat, or a problem with the ignition system. It's best to contact a professional HVAC technician to diagnose and fix the issue.
Thermocouple is probably bad and needs replacing.
dd
Its out of gas
get a new engine DUMMY!
lack of fuel
check ignition
to me it sounds like your map sensor is going out, you might want to check that.
weak fuel pump.
dirty carb bowl or water in the carb
you can but it wont stay running if the battery is dead
check for a vehicle theft system?? Is the Light Illuminated. does it stay on:::
Have you checked the alternator?