Are you sure the air compressor needs replacement? If it runs it probably is ok and I would check for a leak, a faulty check valve or dump valve. Do you have the Gast compressor that AS put in the earlier years? If so, it is an excellent compressor and it should run forever.
I had a similar issue where my pump ran and never shut off. It was a bad check valve which is external to the Gast compressor. This is a generic part that I just picked one from Granger. The compressor also utilizes a dump valve which unloads the pressure off the compressor heads when it shuts off. This is also an external part.
I'm guessing that if your compressor runs and doesn't shut off, there is a leak somewhere in the tubing, fittings, dump valve, check valve or the pressure sensor switch.