If it's like mine, it has a bypass screw in the thermostatic valve that allows the flame to stay lit after the interior of the fridge reaches set temperature and the thermostat cuts the flow of gas to the burner. These screws, according to the service literature I've read, can get dirty and allow the burner to go out when the set temp is reached.
This applies to an RM190 made in the Reagan years, so it might not be relevant to your situation.