The certified flight instructor and his student were practicing a 180 degree autorotation with a power recovery to a hover, when the helicopter's sink rate increased dramatically in the flare about 40 feet above the ground. The flight instructor called for a go-around and increased power, raised the collective, and pushed the cyclic forward. The helicopter continued to descend and contacted the runway in a level attitude. After it came to a stop, a vibration was felt and the instructor confirmed that the main rotor blade had struck the tail boom. The instructor reported that there were no mechanical deficiencies with the helicopter.