Your A/C system has both high and low pressure switches. Being either
over- or under-charged will cause the compressor to shut off.
You also have a thermistor in the evaporator which will shut off the
It's also possible that the ECM will shut off the compressor under heavy
throttle. I haven't checked your particular car, but I know this system
exists on many Hyundai products.
If you're unsure whether it's the compressor, connect a test light between
the compressor electrical connector and ground. Lamp off means the
compressor's receiving no power to engage the clutch.