Here's a stretch and it's unlikely it's your problem. A previous 5er had a kitchen slide out (stove, refrigerator). Whenever I'd leave on a trip, I would light the refrigerator and everything seemed to be okay. After driving a couple hundred miles or so, at the stop I would find the refrigerator not working. As with yours, the stove worked fine.
When we get to a campground and set up, the refrigerator worked fine (on gas or electric).After replacing everything but the rear tail lights <g>, I finally discovered that the flex hose for the refrigerator was kinking when the slide came in. There was enough gas in the line to light the flame but, after some time, the gas in the hose ran out. After some readjusting of the hose the problem was solved. Who woulda' thunk?