Hi my name is Robert...
It may not be a simple fix. It could be an issue with the LP, electrode, or circuit board.
When you troubleshoot these it is a process of elimination. Assuming you have good LP pressure (only way to know is check with a manometer) then it could be a circuit board or electrode issue, the electrode will send a signal to the circuit board when the flame is going, once the board does not see that signal then it will shut down. You need good LP and spark for it to stay running.
IF you have an outside access panel remove that and locate the circuit board, pull the connector on the board and make sure the contacts on the board are clean, you can use a pencil eraser to clean the contacts. Next I would have a RV shop test the board to see if it is the problem, most RV shops and stores have a special board tester so you can remove the board and have it tested, if the board test good then I might replace the electrode.
Some RVS do not have an outside access panel, it will just have an intake and exhaust, if that is the case it makes it more difficult to get at the board.
IF you like I can send you a service manual but need to know the make and model of the furnace.....