It sounds like you're drawing your battery down below 9 volts using too much current and the LVC, (low vlotage cut-off), is shutting the motor off. You didn't say what size prop you're using or how many amps your system is using. Are you sure the battery is fully charged? What condition is the battery in? i.e well used, brand new??? A watt meter will tell you exactly what's happening as you throttle up your system. If you don't have one yet, I'd suggest making it your next purchase. There are several reasonably priced units on the market. If the watt meter saves you from ruining one LiPo, it's paid for itself. Good luck.
Rick