Since you have a 2013 unit, it is about time to take your camper back to the dealer for warranty work.
The thermocoupler above the pilot light usually needs to have the flame of the pilot light in direct contact to keep the safety valve open,which allows the burner to operate. The heat from the burner might keep enough heat on the thermocoupler to accomplish that, but then eventually the thermocoupler could cool down enough to shut the safety valve without the direct flame contact of the pilot light. It would be interesting to see if a higher oven temperature might keep the safety valve open.
Don't have any idea why the pilot light would go out.
Chap , DW Joy, and Fur Baby Sango
2006 Ford F150 Super Cab 4x4
2008 Surveyor 263