The most likely causes are:
* Low refrigerant: This is the most common reason. A low refrigerant charge reduces the system's ability to maintain pressure, leading to it cycling off under increased engine load (acceleration).
* Compressor clutch issues: The compressor clutch might be slipping or failing to engage properly under load.
* Electrical problems: A faulty wiring harness, switch, or relay could be interrupting power to the compressor.
* Belt problems: A worn or slipping serpentine belt can prevent the compressor from receiving sufficient power.
* Pressure switch problems: A malfunctioning high or low-pressure switch might be shutting the system down prematurely.
You need to have the A/C system professionally diagnosed. Ignoring the problem could lead to further damage to the compressor or other components. A qualified technician can identify the exact cause and perform the necessary repairs.