A/C unit cycles on and off during cooling phase
Could well be it is overheating and shutting down.  Have you had the Freon checked lately?  You can put a food thermometer in an vent opening; if the temperature at the vent is over 65 degrees Fahrenheit it is probably low on Freon, and the A/C unit is trying to run 100% of the time to try to cool down.
This happened to me, and the repairman said that was the cause for my situation.  Worked like a charm after the recharge.