I have experienced this only once in my car ('09 LTZ). I turned on the A/C switch and nothing happened. Then I turned of the engine, tried it again and it worked fine. I also had this happen only once on an '07 Impala LS which is one of our office vehicles at work. I think it was caused in both cases by a sticking A/C relay. Obviously an infrequent occurrence. If the a/C relay does not properly engage, no current reaches the A/C compressor magnetic clutch and the clutch will not engage and the A/c does not work.
If the system pressure is too low, as for example caused by a leak in the system, the low pressure switch will not allow the compressor to come on. A rock can hit your A/C condenser int he front and cause a leak. This is easy to check by using A/C gauges to see what the system pressures are.