Power problems stacked Arduino shields
Those 9v batteries are not known for their ability to supply current. Their best uses are long-term powering of low-current standby devices like smoke detectors. I'd first try replacing it with 4 double- or triple-A cells, whatever you can scrounge up for a quick test. My guess is when you cover the robot the Xbox receiver's current demand increases just enough to crash or reset something. A-cells may supply enough more current without the voltage sagging.