Why don't they fly with transponders on during training, precisely for this reason?
It was inop at the time: "The jet’s transponder, which usually helps locate the aircraft, was not working “for some reason that we haven’t yet determined,” said Jeremy Huggins, a spokesman at Joint Base Charleston. “So that’s why we put out the public request for help.”
That being said, no casualties, loosing a stealth fighter is somewhat funny.