Jet engines control themselves by monitoring internal pressures. At high altitudes, the thin air passes through at such a high velocity that the fire gets blown out just like a birthday cake candle. The good ol' P&W engines on the airliner I was on were engineered well enough to accomodate it.
They probably had the misfortune to have engines from Generous Electric! I know an ex-employee that won't even buy their light bulbs (not a personal grudge, he just figures anything not made by GE's got to be better than the corresponding GE product).