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I have a 2000 Jeep Cherokee 4.0/6cyl.  When I shut off the ingition,  the air conditioner will, at times, continue to run.  I have failed to notice this on one occasion, depleting the battery.  The problem is intermittant; it only happens about a third of the time.

My first thought was the switch on the steering column that controls power to the the accessories, but when I jiggle the key switch, there is no difference in the problem.  

Also, this problem does not seem to affect any other accessories, just the a/c.   The main rotary switch on the a/c control panel does not seem to be the problem either, otherwise you would also expect some kind of response in cycling it during the problem, which is not the case.  

Could this be a relay?  

Change the 5 dollar relay.