I'm no expert, but my gut feeling tells me this is a BMS related matter, I agree with nwmtnbkr
1st get a voltmeter, yes i absolutely agree. find out what your battery voltage is at when fully charged, that will give us an idea what we're dealing with.
2nd I would get a cycle analyst hooked up,
then , i would use the analyst to control the max amperage drawn.. you are bound to hit the sweet spot . start with 40 amps and make your way down as the problem persists.
how do i know? because i gots the same behaviour on my 72 volt system. if i throttle too fast from standstill, too much current is drawn to propell the bike from a zero velocity, and this leads the bms to shut down,
in fact for that exact reason i added a push button normal close switch which i use to disconnect the battery from the controller. so when the bms shuts down, i perform a reset using this switch so that i don't need to physically disconnect the wires etc etc and interrupt my travel
nwmtnbkr poses a good question.. what happens when you throttle slowly, meaning as the bike picks up speed and presents less rolling resistance, squeeze the throttle gently .. the theory being, you draw less amps all at once and you don't irk the bms , that should keep you rolling. you should be able to go full throttle once your bike is moving at an adequate speed.
i don't think it's a throttle issue. all the throttle is : it's three wires, basically. one ground, one 5 volts coming from the controller and the third is a percentage of that 5 volt coming back from the throttle going to the controler. as you squeeze the throttle you change the resistance and draw a percentage of that 5 volt which is what that third wire is.. therefore that third wire has 0 to 5 volt on it depending on the position of the throttle and the controller translates that voltage signal to a percentage of your battery's voltage and sends it to the motor. simple and if that throttle were malfunctioning, the kinds of symptoms you'ld get would not be a shutoff of the batteyr but more like the bike stuck on full throttle or not starting at all, i.e some kind of pinched wire shutting off the 5 volt signal to or from the controller
ok, so once you've hooked up a cycle analyst and controlled how much amps you're drawing form the battery .... and you've gone as low as say 20 amps, and the problem persists.. then i would have to conclude that you've got a problematic BMS or the battery is not correctly balanced. I know this is kinda hazy in its description, but i'm no electronic genius
i'm not an expert, just lived a few of those moments and what i've told you so far is based on experience.
in effect i've repeated what nwmtnbkr said but corrolated it with events that have occured in my ebiking experience
keep on truck'in

letuce know what you find (and yes i know it's let us and not letuce

)