Ok this may sound funny but I had to use my furnace in my 2009 3300SK lastnight in Southern California. I have used it may times before with no problems but lastnight it would kick on and then shut off. In the morning I went outside to see if I was out of gas and I wasn't. Could this be a ignitor problem? I had to change out one in my flagstaff but I do not want to start ripping stuff apart. It just seems that it's not getting any fire to light or gas to light?
I probably am not going to say this right...but, it sounds like you have a microswitch problem on the exhaust. The flue has a flutter valve that opens when the heater turns on...and closes after cool down. If this switch is not operating properly, you will get turn on, the fan will run and the heater possibly might ignite. If the switch does not make contact the heater will shut down. This thing is there to keep you from setting your trailer on fire...and to keep noxious gasses out of your RV. So, if that switch is bad, you get a partially working furnace.
Also make sure that the flue is not blocked and that it will open and close manually.
You did not say whether your heater had a pilot light or not. There are times that the orifice on the pilot light gets partially blocked and will not have enough flame to light the main burner. Just clean the pilot light orifice and it should work.
On the microswith above, it will have to be replaced...but, you should be able to jump around it in the circuit to test it out.
Finally, make sure that you have 12 volts going into the furnace. In my old airstream, I had a high impedance short in one of the 12volt lines...if you measured it...you got about 7 volts. And you will get the same symptoms as if the flutter valve switch is not making contact.
Best of luck with it...these furnaces are not easy to work on.