Yup. You have ALC (Auto-Level Control) suspension and those air sleeves on the shocks are deteriorated. The usual chain of events is they wear through and leak and the compressor runs more than necessary. The leaks get worse and the compressor eventually runs itself to death. You can replace the shocks and compressor and it'll probably pick up where it left off. OEM shocks, if they're even available, will be really expensive. An aftermarket compressor unit is about $200 last I checked. The shocks have electronically variable valving in addition to the air sleeves. Most, if not all aftermarket shocks that have the air sleeves bypass the electronic valving with a built-in resistor. So the aftermarket shock will connect just like the original with the air and electrical connections, but the variable valving portion won't be operable. The resistor is there just to keep the StabiliTrak and Traction Control Systems happy.
So, if you don't or rarely tow, or don't tow or carry much weight, you can disable the ALC system by removing fuses and install some ~$12 resistors to bypass the other systems. Then, install whatever quality "dumb" shock you want. Bilstein 4600 series are pretty much the #1 choice for this. Lifting or lowering will alter your shock of choice, if either of these are in your plans.
