If you did not replace the condenser at the same time, you likely have some debris from the original compressor escaping and destroying the new compressor. From what I was told, our systems do not flush reliably and the condenser must be changed.
I had an issue where my compressor went bad, so I changed the compressor, expansion valve, and dryer. Three weeks later, the new compressor started making a high pitched wine and there was no more cold air. The next time I was told that I need to replace the condenser, dryer, and compressor - it has been three months and everything has been working well now.
Essentially, add the compressor to the list of what you have ordered and go for it. Try 1-800-RADIATOR, because they can put a kit of all of it together for you. I was able to use a friend's account and only paid $530 for everything.
NOTE: Replace the oil in the compressor to make sure it is clean.
2009 Jeep Commander Sport 3.7L V6
Upgrades: K&N Filter, DRL's, Rear Handles, Curt Hitch, Steel Suspension Skid Plate, Fogs, Secure Console Cover, Bilstein 4600 Shocks (F/R), Moog Front/Rear Swaybar Links, Moog Front Swaybar Bushings, Moog Front Lower Control Arms, EBC Greenstuff Pads, Ignition Mod