I really have no idea, but heres to guessing.
What Andrew said sounds correct.
And im going to go on and take a random stab...
Burning hydrocarbons needs the hydrocarbon itself and O2, oxygen. When the supply of oxygen is limited, such as at high altitudes, the extent of the reaction would be limited too.
So a lack of oxygen would lead to a lack of the overall reaction which would lead to a flameout. I will take another step further and say temperature and pressure also have a pretty important role as well. Temperature and Pressure are proportional to kinetic energy. A specific amount of energy for a reaction to start is needed (activation energy), so a certain amount of molecules must have equal to or greater than the Activation Energy for the reaction to proceed. So if Temp and Pressure are decreased, so will the amount of energy.
So lower temperature and pressure at the increased altitude, as well as decreased oxygen could all play a part.
This is all guessing by the way, so im probably wrong
