G80 is locked ALL the time

I had my 2006 2500HD D/A into the dealership a couple times under the 3y/36k mile warranty with a complaint of the rear differential locking and not disengaging. Both times the dealer claimed they could not duplicate my complaint. One time, the rear diff was locked as I pulled out of the dealership.

51k miles on the truck now and the rear differential has been locked and not disengaging for some time. The truck chirps and/or shutters a wheel ALL the time when going around corners and always skids & shutters one tire when pulling onto my dirt driveway from the paved road. The rear tires have been wearing excessively since the differential locked up, but I don't like the tires on the truck right now so I haven't been too worried about it. Looking to change tires in the near future so I'd like to get the rear diff problem resolved.

I have changed the rear diff fluid a couple of times since I bought the truck new. I used the proper fluid each time. No diff leaks, it's never been run low on fluid, never overheated, never abused (burn outs, etc). The most it's seen is a regular ration of pulling ~7k trailer.

1. Is the locked diff still under some sort of warranty? If not, do I have a legitimate gripe since the truck was into the dealer 2x under the 3y/36k warranty for the same issue?

2. Any idea what would cause the diff to lock and not disengage?