The helicopter landed hard after a practice autorotation with a power recovery. At approximately 550 ft AGL, the CFI announced a simulated engine failure to the ATP and the throttle was closed to flight idle. The ATP entered an autorotation smoothly and turned left rapidly into the wind. During the turn, the rotor RPM began to increase and the CFI increased the collective to maintain rotor RPM within limits and then reduced it. The ATP began to decelerate at 300 ft AGL and airspeed began to decrease. At 55 knots indicated airspeed, the CFI called for a power recovery. The rotor RPM began to decrease and the CFI got on the controls and attempted to execute a power recovery. The ATP had a tight grip on the throttle in the override position. The CFI was unable to twist the throttle to the positive range position. At 100 ft AGL, the CFI noticed low rotor RPM and an excessive rate of descent. The CFI flared the aircraft and attempted to cushion the landing but the aircraft landed hard.