The flight instructor reported that during an instructional flight, the helicopter was at 500 feet above ground level when he rolled the throttle off with the intent for the student to respond by initiating a straight in autorotation. The student pilot did not respond properly, so the instructor took over to initiate a power recovery. The helicopter subsequently landed hard, deforming both skids and substantially damaging the airframe. The pilot did not report any preimpact mechanical malfunctions or failure with the helicopter that would have precluded normal operation.