All* properly running A/C systems will cycle the compressor on/off while running. This is done to prevent icing on the evaporator while still providing cold air. Low refrigerant levels or blockage of airflow across the evap or condensor (clogged filters, for example) can cause the system to not cycle and also not cool properly. I bet what you sense is the off cycle when the humidity/temp returns to the air temporarily.

*Some of the latest ultra high efficiency compressors do not cycle. They have variable displacement to adjust their cooling capacity based on demand. The Chevy Cruze ECO and some others do this instead of cycling on and off. Some of them are not clutched and always run, even when the A/C is 'off'.