You could disconnect the power wire at the receptacle and run a new (fused) power wire to it.
I chose to keep the stock receptacle switched as it was. I did add 3 always on receptacles and a USB power port. I installed them in the slot below the radio.
I keep a rechargeable trouble light plugged into the switched receptacle. On occasion I have a GPS, satellite radio, radar detector, and cell phone plugged into the added receptacles.
NE Ohio - home to the most successful Pontiac drag racing team in history - Bill Knafel's "Tin Indian" and also home to Summit Auto Racing.
2009 Vibe base 1.8L auto towing 2009 Aliner Sport hardsided pop-up
In the diagrams that strangerxp posted, 5 shows the lighter (12V outlet). It goes directly to the CIG fuse, and from there to point Q in diagram 3. It works backwards through the accessory relay, which is controlled by the ignition switch. Theoretically you could replace that accessory relay with a jumper wire, but then your radio, amp, and outside mirrors would always have power. Years ago I had a car where the radio wasn't not switched by the key, I recommend against that.
On the 03-08's the cig lighter is wired pretty much the same as in these diagrams. the 03-04's had a second 12V power outlet between the seats, and it is easy to add it to the 05-08's since the wiring is all there. This second outlet is controlled by it's own individual relay, and that 's the one to replace with a jumper to leave the outlet powered on all the time. There is no direct equivalent for the 09-10's, so if you want the lighter outlet to be on all the time, your pretty much need to do as beemerphile1 says, just run a new constant 12V to the lighter.