Suggest you go to
Chris Bryant's Site. Find your model and look at the installation instructions. You'll see some very specific DO's and DONT's, some of which involve whether your fridge is in a slide or not.
Also please look at the fridge's lighting algorithm. Most modern Two-Way RV fridges (LP Gas/120 VAC) will make several tries to light LP. Those tries may be a series of attempts. But in the face of continued failure, the lighting process "locks out" and the user has to cycle the switch Off >>> On to get a new series of attempts. So... if the flame is blowing out, the fridge should be trying to re-light. After a long drive, with flame blowing out repeatedly, you might find the flame lit BUT the fridge warm inside when you stop. When you drive with the fridge in LP mode, is it lit when you stop? Are the external coils of the cooling unit warm/hot?
You ARE leaving the House Battery in your Trailer ON while traveling, correct? Those modern fridges have a "Lock IN" feature where they'll run the gas flame as long as the LP lasts, even if no battery power. No thermostatic regulation either, so freezing the whole fridge compartment is also a possibility. BUT if you turn the 12 VDC power off, the fridge locks IN, then blows out, it won't try to light again till you restore 12 VDC...
If you arrive with flame lit, coils hot, fridge warm inside, then it's an install/venting problem or defect in the fridge.