2001 Pontiac Aztek Lift Gate

You could have one of a few problems. You could have a faulty release actuator, broken wires from the body to the liftgate or you could have a faulty BCM, Are you experiencing any other electrical issues?

No, I am not having any other electrical problems. How would I check for broken wires or a faulty release actuator?

You can check to make sure there is power at the fuse, but if you remove the tailgate panel, it has a few screws and a few retainers, you can check with a test light at the actuator, lt blue wire is power and black is ground. The lt blue should only have power when you hit the release. You can check for broken wires in the boot from tailgate to body... the easiest way to check would be with a scan tool where you could command it open. You would be able to tell if the circuit or the actuators were bad, or the BCM.
If you don't feel comfortable with all this, I am sure your local gm dealer could figure it out. If you were in the Oshawa area I could have a look for you.