Does it actually power off?
Or does it just stop responding to the throttle?
If the former, then the battery's BMS is shutting down to protect itself from either overdischarge (too much voltage drop in the cells under load, which you won't usually see *except* under that same high load) or overcurrent. You'd have to find out which, and proceed from there.
If the latter, then there are at least two possibilities, potentially several more.
First, the controller could be setup wrong for the throttle you have. When throttle is above some particular voltage, it could be triggering "high pedal fault" or something similar, where there is too high a voltage on the throttle input so it stops responding because it thinks the throttle is broken and may be stuck on full.
Second, the controller could have it's LVC set to such a high voltage that when the battery voltage sags a little bit under high current, it shutsdown to protect the battery.
Other possiblities include a current or power fault limit in the controller's settings that when exceeded cause shutdown ratehr than simple limiting.