I vote for damaged cells. It can explain the low maximum voltage and high voltage drop during any load!
Yes this is what the test with voltage probes on pack when twisting the throttle looking at the voltmeter is for.
I was thinking it could be a short in the motor drawing excessive current.
I do believe the controller has a safety off function for a few things too, overheating and other stuff.
He must rule out the charger,
BMS or cells first.
Another test is a load test.
4X 15v 150 watt halogen bulbs in series.
Place four of these in series between both pack output terminals and use an amp meter to test load, These draw almost 15 amps and output almost 600 watts on a full pack, You only need to test for 5 minutes or so. More than 45 minutes and the battery may LVC. All lamps will get very hot so be careful.
This can work as a capacity test too.
With no controller connected and lamps placed over the terminals, the above test will weed out the bad packs from the good ones with no problems or chance of mistakes, providing human error is not any cause of failure.
The above 15 amp load test will test everything from the pack battery output,
BMS, and detect possible battery terminal or cable intermittent failure.
I find dry joints in old TV's and stuff by tapping the operating circuit board gently with the plastic butt of a screw driver and observing the screen in a mirror. A singe flicker or noise crackle from the speaker and I mark the area of the PCB I was tapping and resolder the area.
I would do similar tests on an intermittent controller to see if a bumpy ride would cause me grief.