VERY common problem on the 09-10 models. My former 10 GT had the radio replaced twice under the 3/36 warranty due to the bad knobs before I bought it. They are a cheap design and fail often if used a lot. Mine broke once more after I bought it and I ended up replacing it with a modified one to avoid having to take the radio apart. Luckily I had the steering wheel controls so I never really used it for the volume.
If you are somewhat handy, you should be able to replace it yourself for less than $10. GM sells the knob separately.
Here are the steps to fix it, taking the radio apart, and not taking it apart by cutting out the knob and removing the flange like I did.
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Good luck!