The flight instructor was preparing the commercial rated pilot for a check ride in the helicopter equipped with skid type landing gear. During one of three running landings to a touchdown, the flight instructor was demonstrating a practice hydraulic failure running landing and the helicopter started to get into ground resonance as he initially touched down. The flight instructor increased power to become briefly airborne and continued the maneuver to a normal practice hydraulic failure running landing. After the ground resonance experience, the flight instructor continued the flight training session for an additional 45 minutes and conducted another hydraulic failure running landing, several slope landings, and five hovering autorotations. Two of the hovering autorotations were described as rough, with an undesired drift to the front left. The flight instructor then left the airport where they had been practicing and returned to their home base airport where they conducted two straight in autorotations, and three 180-degree autorotations, all to a power recovery. After shut-down procedures were completed the two pilots were surprised when they discovered damage to the helicopter. The helicopter was substantially damaged with buckling around the full circumference of the forward part of the tail boom and a crack in the skin at the 6 o’clock position. The flight instructor stated that he thought the damage occurred when they were conducting hovering autorotations. The two pilots reported that they were not injured.