Pilot light on GE water heater goes out when burners go off. I'd hate to replace the thermalcouple if that isn't the problem cuz it comes in a pilot assembly and costs about $40.
Try and tighten up the nut that goes into the regulator. That may fix it if not go to a box store and get a thermacouple like was mention around $10.00 . The universal will work length doesn't mean anything as long as it is long enough . If you have to get a longer one juse put a big loop in it . Don't kink it tho. good luck have fix many of them nothing to it