Refrig Problem

Short answer, that shouldn't be happening. I haven't had to deal with this complaint very much. Since I don't know what model refrigerator you have, I will be pretty generic here.... But I have to ask,(I don't mean to insult your intelligence, it's how I diagnose, I start at the very beginning and assume nothing) how are you determining the flame is out? Is the check light on or are you listening for the faint flame sound? It is normal for the flame to cycle on and off, so if you have been traveling no one has been opening the refer it mighthave reached set temp and shut off (unless your refrigerator uses a high-low flame to regulate temp).
If not that, how does the refer work? OK or just so-so? If so so you might have a weak flame, lots of causes there, but a week flame will blow out easier and provide a weak signal, so the brain will be quick to shut the gas off.
Then we have the shielding. Is all the factory sheet metal in place? You might have to do some comparisons with similar units to make sure.
I have seen some exterior doors with model specific sheet metal on the interior, any chance the exterior door has been replaced?
Hope this helps you.

Wish I could help. The guy we bought ours from said to turn the fridge off while towing so we've never tried it to see what happens. I also turn the propane off at the tank in case there's an accident. We keep the fridge cool by putting a few frozen 2 liter water bottles inside. Good luck!

The 2 liter frozen water/ice bottles do the trick to keep everything cold during the day. We've been on the road as long as 14 hours like that with no issues. When we stop for the night we use propane or shore power - whichever we have. This re-freezes the water bottles for the next day. 

Another option is dry ice in the fridge. Most of the grocery stores and Walmarts around here sell dry ice. A pound will last all day in the fridge to keep it cold but we've found sometimes that it's too cold and the milk will freeze. To get around this sometimes we'll put dry ice in an Igloo type cooler with the water bottles. It'll freeze them down to much below 32F and keep the fridge cool even longer.

Hope this helps.

OK, yours regulates temp by varying flame size, so when it goes to low flame it blows out, which is pretty easy, as it's a small flame, even when on full. If I remember right, there has been various fixes for this, ranging from metal shields in the exterior doors that calm the wind down, to putting blocks of ice in the refrigerator compartment to ensure temps stay low, which really isn't that hard to do, as these refrigerators will hold a good temp for a fair amount of time, generally long enough for a day's worth of travel.   
 

First off, an RV tech needs to check the gas pressure, flame & thermocouple placement & shielding to make sure your refrigerator is totally up to specifications, as "looks good" can get you in trouble because the flame is so small to start with. Checking gas pressure requires a gauge the measures in. of water column as well as some training, so best leave that to a pro. Assuming you got the installation booklet along with the owners manual from your dealer, you can verify the installation is within spec, as far as distances from interior wall, location of access doors. If you didn't get it from your dealer, most are available online.
I am being cautious here because blocking air flow to the refrigerator can cause issues ranging from poor cooling to causing a fire, so this needs to be approached slowly and carefully. With all that said, what I remember seeing was a piece of sheet metal about 3-4" high across the interior of the bottom of the bottom access door. I think what it did was calm the air, as air could still enter thru the vents, but was deflected upward.

You are welcome, I wish I had a solid answer for you, fixing them with just a keyboard is tough. Please keep us advised as to what the final fix is.