P2101 P1516: Solved
 

I realize there are threads about this subject in different places, but wanted to document my experience in hopes that it helps folks in the future.

I have a 2009 LS3, Manual, bone stock. a couple of weeks ago, at highway speed, the car went into reduced power mode. This was accompanied by a pretty rough idle with bouncing RPMs. I turned the car off and restarted and the issue was gone. I pulled the codes when I got home: P1516 and P2101. I cleaned my throttle body (which looked almost corroded on the blade) and the issue was gone for a few days.

After a few days, the issue was back. Eventually the issue occurred more and more frequently. The bouncing RPMs (almost like a big cam lope) in reduced power mode at idle did not feel right, so I assumed something was amiss in the servo motor of the throttle body or that it was not closing properly. I ordered a replacement on Amazon for $150, and it only took 10 minutes to replace. The car drives like brand new.

GM throttle bodies are known to do this, it would seem...
I had a day in winter when I started my truck (2010 Silverado with L9H (95% the same as an LS3)) and it did the rough idle thing and threw codes at me. After checking around on the Silverado forums, it turned out to be the same thing you described, and others simply replaced the motor on the throttle body as you did. In fact, someone posted a youtube video of tearing down the entire throttle body and placing every piece under a microscope to find out what was failing, and it has to do with some metal contacts inside the motor... Anyway, I had my LS3 throttle body laying about doing nothing, so that was a 10 min swap onto the Silverado and it ran fine after that. Definitely cheaper than buying a whole new throttle body assembly.