As one of the answers said,replace the thermocouple first.As long as there is a flame on it,it creates a small electrical current to keep the gas valve open.No current or a weak current will shut the valve.

follow the gas tube from the conrol valve down into the burner compartment……..Ok along side that you should see what looks like a thin copper wire that starts out at the control valve and ends up in the pilot flame….. that is called a thermocoupler it sences heat it is probably not sitting in the flame properly or crudded up or just bad…..its a safety device if pilot flame goes out it will shut the control valve off to stop the flow of gas……they can be changed fairly easy cost about 10 – 15 dollars

air in your lines
a leak in the lines causing lower pressure
a bad solenoid (gas valve)
a partially clogged orifice (where the gas comes out for the flame)

but most likely a problem with the thermocouple (flame sensor)
it looks like a metal wire that sits in the flame, it is a bi-metal rod that produces electricity when heated, you can clean it off with emery cloth or steel wool, the carbon deposits may block some of the heat causing the sensor to think the flame is out and then it will close the gas valve.

Shut down the gas line Clean up the aluminum gas tubing the one hooks up at the gas regulator it might be full of powder stuff then replace the thermo coupler into a new one.Put it back together then re lit the pilot.

Your gas valve/thermostat has gone bad. The small magnet inside the valve that holds the flap open to allow gas to flow to the burner, gets weak. No one seems to be able to tell me why this happens, but it does. Unfortunately there’s no repair for this condition, just replacement of the complete assembly. Depending on whether your unit is natural or LP, the valve assembly will cost between $170 – $225. It’s not terribly complicated to change, but you must drain the heater, as the valve screws into the side in a 3/4″ opening. You must, of course, remove and then replace all three of the connections on the underside of the valve.