Depending on how cold it is and sometimes how full the tank, starvation with gaseous fuels is not uncommon. When our CNG car gets low, the tank will chill due to pressure drop sometimes to the point of engine stoppage, then will restart a few minutes later its fine.

Your propane tank would have to get down below -40F or so to stop delivering vapor at all, but it may chill enough to not deliver sufficient amounts to run the engine at normal power.