I don't believe there is an emergency beacon on the bird other than in the chute pack in the case of ejecting. A simple crash while doing NOE flight (it was a practice flight) would be below radar, if there is a radar covering that area, and would preclude any ejection beacon. There is also the possibility that the beacon had a dead battery or was simply defective to boot.
Had there been a defection, and I find that to be a very unlikely possibility, there wouldn't even be any news that a plane was missing at all. At least until the folks that have it decided to brag about it.