Low refrigerant can plague nearly any type of air conditioner compressor. Refrigerant must maintain a steady pressure in order to function correctly, but small leaks over time can drop these levels. In such a case, the refrigerant will start flowing a little too quickly, performing certain cooling steps too well. This leads to rapid shutting off and starting of the compressor as it tries to compensate for the rapidly moving refrigerant. To fix this problem, call a professional for a measurement of refrigerant pressure and any necessary changes.
In some cases, a compressor that shuts on and off repeatedly is being affected by electrical issues. Problems with wiring and circuit boards can create mismatched signals to the compressor motor. As a result, the motor will start over and over, but the compressor will never be able to fully turn on. If the wiring fails further, the compressor will stop working entirely. If you have a multimeter you can test the wiring that leads to your compressor or hire a professional to test the system for you. The motor or at least the wiring will probably need to be replaced.
Air conditioner units are sized according to the amount of space they must cool. If your air conditioner is sized too large for the space it is in, it will cool the air too rapidly. Large-capacity air conditioners are not always best. The unit will turn on and off very quickly as it cycles on, cools the air too rapidly, then shuts down again. Eventually it will make false starts as it receives conflicting thermostat information. Worse, only the area immediately around the air conditioner or A/C vents will get cool. A sizing issue can be solved only by switching to a different furnace, properly sized for the cubic feet of space in your home.
Weather can affect compressor operation. If ice forms on the evaporator, it will not be able to release heat effectively enough for the compressor to work. The compressor will keep trying to send refrigerant to the evaporator; but since the evaporator cannot handle the job, it works too long and the compressor begins shutting on and off in an attempt to regulate refrigerant flow. If you keep your evaporator clean and protected, removing any accumulated snow or ice, both sides of the system will function better in the winter months.