During a practice hover autorotation, the helicopter touched down hard. It subsequently experienced a dynamic rollover, coming to rest on its right side. The certificated flight instructor (CFI) reported that the purpose of the flight was to conduct training for the student pilot (positioned in right seat). The student performed three hovering autorotations without incident. On the fourth autorotation, which was to be the last of the flight, the student entered the maneuver properly. The student then made several cyclic input changes and the helicopter touched down on the left skid, resulting in the helicopter bouncing back airborne. The student reacted by inputting left pedal followed with abrupt right forward cyclic movement. The helicopter drifted right and began to pivot around the front portion of the right skid. The CFI assumed authority of the flight controls in attempt to regain directional control. The helicopter rolled over on its right side. The CFI reported no mechanical malfunctions or failures with the helicopter prior to impact. The CFI stated that his total flight experience totaled 507.6 hours, of which 279.2 were accumulated while acting in the capacity of a flight instructor.