Everything stays firmly on. All power supplies (4.72V) stay up, as does the 41V into the controller. The lights on the display all stay up with full battery indicated. My test is to tilt the back wheel off the ground and twist the throttle. The wheel rotates at a good rate. I then lower it towards the ground, just touching, and the wheel slows. Firmer contact with the ground will result in a sudden lose of power and lifting again from the ground, the wheel rotates very slowly. This will not recover until the system is switches off and on again. Through all this the lights and power supplies stay on.
OK, that's quite unusual. something is messing up the controller. it could be a fault in the controller or in the motor cable. The motor cable is a little tricky to repair, but can be done. Without another motor to try, I would take a gamble on the controller, though my suspicion is that it's the cable that has the fault. You can get a bit of extra chance by buying a dual-mode controller that can run with and without the hall sensors.
I'm pretty sure that this one is compatible with your existing display. You'll have to change the connector for the hall sensors or try running sensorless without them connected first. I think all the other connectors are right, but you should always check that the wires are in the matching sequence in the connector.
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Alternatively, you can use the Brainpower one that comes with an LCD for not a lot more, though there might be a bit more that you have to do with connectors.
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A new controller will fix it if the problem is in the controller or if it's one of the hall wires that's damaged. I think if it is a damaged cable, it's more likely that a hall wire is damaged than a phase wire because of their size, so I reckon the controller has about a 70% chance of fixing your problem as long as your motor runs OK sensorless. Some are better than others, but I think yours should be OK. It's the high reduction ratio ones that give problems the most. The KU65 has always been pretty good at sorting out difficult motors. I don't have any experience running sensorless with the Brainpower one.