No, it is the low pressure switch that should be turning the A/C on and off (and in turn the relay). The A/C is SUPPOSED to cycle, it has to, just not too fast. Basically, as the compressor runs, it gets colder, which means the pressure inside the A/C system continues to drop. Once it gets to a certain point ~20 PSI, it shuts off until the pressure raises, to keep the evaporator from freezer (and also to prevent the compressor from running without lubrication which happens at low pressure). There's no set number of seconds it's supposed to cycle - depends on temp, fan setting, engine RPM's, speed, etc. But above 65 degrees while driving, it probably shouldn't cycle on and off more than every 6 seconds or so.

Only if it's really really hot out would the A/C never cycle.