I have only tested this library with a wired XBOX controller and a Joystick because they are the only devices I have. I assume the wireless controller is powered through the USB port but the actual controller is battery operated so will go to sleep if not used.
You might try
//when the controller is disconnected and i turned it on again
void mousePressed(){
//close the device or dispose or proper way to do it...
xbox.available = true;
//and set it up again maybe like so
xbox= control.getMatchedDevice("360");
}
If this doesn’t work then I can’t think what else you might try.