Hi coolydee
This is a odd one, we have had a few questions about wii and ps3 controllers not staying connected but I think this is the first xbox example.
A few questions first:
Do all your normal xbox controllers stay connected?
Do you have any other instruments that do or do not stay connected?
Have you tried taking the guitar to a friends to try it on their console (you do not need the game to connect the guitar to the console)?
Answers to these would at least let us know if your issue is inside the guitar / xbox / elsewhere.
Thanks for posting
Steve