Hi Martin and
to the forum.
It sounds to me like the battery is very weak and the voltage of one
(or more) of the cells is dropping too low under load and forcing the
BMS to cut the power to prevent it from being overdischarged.
I don't know what chemistry your battery is
(LiMn or LiFePO4), but if it's an 8 years old LiMn battery pack, it has achieved a very good lifespan.
With a weak battery, you should notice that the LEDs will start to go off one after another as more load is placed on the battery
(or more throttle is applied) just before the battery power is cut off completely by the
BMS.
If the battery is old and weak, it probably needs to be replaced
(unless you can find someone with a suitable spot welder who would be prepared to replace all of the individual cells instead).
The screw terminal cells used in the more recent
LiFePO4 batteries are much easier to replace.
Alan