First two things I’d check are fuel pump and battery.
Fuel pump: when the diaphragm wears out it stretches out and stops pumping fuel efficiently. It shows up as miss-firing and hesitation on the track, and if unchecked eventually leads to the engine just dying.
But a bad battery will do the same. If it will not hold a charge it will start out strong and quickly fail to run the kart out on the track. Also a bad battery can have enough voltage to spin the starter but not engage the flywheel and therefore not turn the engine over.
After checking those two, I’d start looking at the wiring harness.