Here's something from another website. It talks about how the compressor is disabled when the pressure gets too high, which can happen during acceleration.
maybe you can spend $20 to get access to the pressure gauge that comes with those A/C recharge bottles? Don't pierce the bottle, just use the gauge connected to the dummy plug to prevent leaks (I think?), connect it to the A/C system and see what your A/C pressure is at. Monitor the pressure when you hit the gas or accelerate, and see if it goes into the red zone.
Here is the quote, but note there is a slight difference in I believe this car used an A/C compressor with a clutch, unlike our Kias I believe that do not have an A/C clutch:
when I rev the engine,the pressures increase and that is when the compressor cycles off,one the pressures start to drop the compressor cycles back on. The pressures it cuts off at are 40 low side and 150 high side. Everytime I rev it and the gauges hit those pressures the compressor cycles off. I looked around and I can not find a high pressure switch,I do however have a pressure switch on the condenser,im assuming its the low pressure switch for when I unplug it the compressor instantly shuts off