My 2000 Grand Marquis seems to leak air after about 5 hours of being parked the back end of the car (for lack of a better word) has deflated.

I have also noticed on ocassion when the car is parked and shut off(This could be after an hour or more after shut off) I have heard the compressor motor come on (or at least it is the same sound car makes at startup). I have also ocasionally noticed the car lowering as if someone was letting the air out. I have only had this car 2 years. Are there any self checks to find a leak. Do these things seem related

 

in my opinion, air ride is a money pit... if something happens to it, it costs an arm, a leg, and first born pretty much for repairs... a decent auto shop can check your air ride with a smoke machine and track down where it may be leaking... many times the lines crack or an air bag gets a hole in it

 

Many CV & GM owners have replaced their air suspension with coil springs due to the high cost of A/S repair. Usually just about everything needs to be replaced including the compressor. The coils ride a little firmer, but the car handles much better without the problems of the A/S.
You might want to check out; http://www.strutmasters.com who carries coil spring kits.