I don't know if this will work for you, but our hot water heater has trouble staying lit when we first use it after the trailer has set for some time. It spits and sputters, and goes out. It takes a little time for propane from the tank to purge the air out of the line, and the water heater is the furthest appliance from the tanks (on our 19-foot Bambi). We just turn the wall switch off for a couple of seconds and turn it back on again. After a couple of cycles like this, the propane has made it to the hot water heater and it will stay lit. This also seems to help the refrigerator start and stay on (when using propane). I never checked the propane lines to see how they are routed, but it seems like if we light the stove first, we have less problems; although this may just be coincidence.
If you are in the mountains and the tank you are using isn't full, you might try switching to a full tank. It seems like more pressure helps, too. This also works in subfreezing weather, when the propane tank pressure drops due to the cold outside temperature (even more of the problems in subfreezing weather in the mountains).