There is a great document in the STAR database that explains the entire air suspension system of the Grand Cherokee, but it is essentially the same design system. It is 23 pages long and although it has lots of reference to WK, it gives a very good description of the proper diagnostic procedures and system operation. Most compressor failures are caused by pinched/leaking lines, or clogged inlet filter. The compressor is not designed to run for very long, and will overheat and shut down with just a couple of minutes of run time.
They can find it by using 2011-2015 WK as the vehicle and search term "air suspension."