The only possible solution I heard of is the hard reset move. It could be a number of things.
Could be a firmware issue that affects a small number of systems (you in the preview program?)
Regardless, a hard reset usually fixes the issue. If the problems persist, call 1800-4-my-xbox and they will run you thru a few troubleshooting moves before determining if its just your Kinect that's faulty.
And that will be covered in the warranty
You just got your Xbox, they usually not that strict with dates. You can also say it started happening after your latest update thus putting the blame on them. Just remain cool, they'll take care of you. Unlike on the sony side, they not trying to get over on gamers on the greener side... usually
XBL? They some stingy b*stards. But system issues they have been top notch from my experience.
Make sure you tell her you love her if you gotta send her away