Leaks in the air suspension can cause the air compressor to run constantly.Google+
Car Problem Reports
Saab 9-7x Air Compressor Runs Constantly
Saab 9-7x Problem
Average Mileage: 60,111 mi (38,000 mi - 109,000 mi)
Visitor, 2008 Saab 9-7x, 38,000 mi
Air pump kicks on when the car is off, keeps killing the battery
Visitor, 2009 Saab 9-7x, 65,000 mi
Compressor stayed on after car is off killing the battery. Small leak in air bag, but issue was with the compressor. Dealer charged 900. for compressor and labor. Air bag was another 400. Bad day.
Visitor, 2008 Saab 9-7x, 50,000 mi
Took out the fuse.