Does it work with the wheel off-ground?
If so, then the load while riding is too high for hte batteries, and the BMS in the batteries are shutting down to protect them.
If there is no BMS, then that means the cells can't output enough current so they drop in voltage so far that the controller shuts down to try to protect them.
1000w at 36v is about 28A. That is a lot of current for a 12Ah battery of most likely very cheap cells, and can be hard on them, so they may not last long. Most likely it doesn't see that kind of current for more than a few seconds at startup from a stop, but it can still affect them over time. If it's used on hills it could see that current for significant time.
If it does not work with wheel off-ground either, then something might be causing friction on the motor wheel, such as brakes rubbing on the rim, or a bent wheel causing tire to rub on frame. On a rear wheel it can even be the sprocket or freewheel pushing against the frame, and the hub or it's plastic "protector" rubbing on the freewheel.
It's also possible something is wrong with the controller itself, blown FETs, etc. If so, you'll find the motor is hard to turn by hand, usually, as the FETs typically fail shorted.
The motor itself could also be shorted--this usually happens when the phase wires coming out of the axle get damaged in a crash or similar, and tend to get cut against hte axle, and may intermittently short to the axle and each other. Again, the motor is hard to turn by hand.