Dometic Refrigerator not running on LP

[Twins]

Hi, everyone! I need some advice. All of a sudden the Dometic refrigerator won't stay running on LP. It works fine on electric and will start up an run for a few minutes on gas before it shuts down and the check light on the fridge comes on. I scraped some carbon off the tip of the thermocouple today and it ran for over an hour without stopping. I know the gas is making it to the burner and the igniter is firing when called. I am suspecting the thermocouple is going bad. I am assuming that just as thermocouples in hot water heaters sometimes need replacing, that the same is true of gas fired refrigerators. Does this make sense and is this a common problem?