Heat will go out after hours of use

You have a gremlin to chase. I'd start with the 12V system to the unit and work out to propane. What I'm thinking is it is not too cold for propane if you are camping in the USA especially if it was "working" then "not". If you figure it out please post.

Last resort without spending $$$$ space heaters are $9.99 at walmart. I know it won't fix the prob and for some it eats at them to not fix the problem but the outcome is warm.

Two possible issues:
One Propane/Butane
Some dealers, mostly in the south will sell you Butane as Propane. In fact I recently watched a TV show where they referred to the system as "Butane" not Propane" (Mr. ED rerun if you want to know, the one where "The Coronal" shows up, His trailer and his wife called it Butane)

The Vapor temp of Butane is around freezing (32f/0C) so if it gets cold, It won't vaporise (Turn into a gas) but instead remains liquid.. No gas No heat

Propane on the other hand a gas down to around -40 (C or F take your pick) but higher to get the pressure you need (Say -35)

So if you have butane in the tank,, Nothing works sub freezing.

Now the other issue: All the systems you cite use battery power

The furnace uses it to run the blower, control the gas flow and ignight the flame. If the batteries run down (The blower sucks MAJOR power)) then the blower wont't run fast enough to trip the "Sail Switch" (Name is Descriptive, A literal sail operates the switch) and the furnace will fail

The Fridge computer may get confused as well at low voltage

And a propane alarm give an error code as well.

Don't overlook 12VDC power. All the items mentioned, water heater, thermostat, furnace and fridge use 12VDC for the controllers. The furnace also needs it for the blower. If you're plugged into shore power you might not notice unless you happen to turn on a ceiling light.

A second potential trouble maker(s) are the CO detector and propane detector. Depending on your coach you could have an automatic shut off valve on the propane line that either of both control. To add an additional twist both are 12VDC powered and I don't know how they would react if power is less than optimum.

Propane can have issues in very cold temps. Here is a good article explaining the limitations and how to accommodate them.

https://www.bournesenergy.com/news/propane-in-cold-weather-800937483

We have never stayed in temps as cold as you are in, but from reading on these forums, it is known that the absorption refrigerators do not operate properly in cold temps. Many hook up a light bulb in the exterior access to help keep it warm enough to work. If the flame goes out, the gas probably shuts off as a safety feature. On the furnace - guessing that maybe after running for so long it overheats, and also a safety feature that it shuts down for awhile to cool off. I do know that our Atwood also has a 1 hr time period if gas valve shuts off because of no propane. Is the pressure regulator maybe going out and when pressure is low, gas valve shuts for the 1 hr lockout. Just guessing at a possible cause based on things ours has done Many problems we have had with any of the gas/electric appliances has been corrected by checking and clean electrical connections make sure everything is tight and cleaning burners, etc. We also had a problem one time when there was a crispy fried mouse near/on the burner area. Remove the mouse and furnace than ran like it should. Have you looked online for a manual and troubleshooting for your particular brand/model furnace. They are very helpful with diagnosis sometimes.