The flight instructor said that during a landing, the student pilot flared too high and that he then took over control of the airplane. The airplane landed hard, and the tail tie-down hook struck the runway and was displaced into the fuselage, substantially damaging the aft bulkhead. Although the instructor conducted a postflight inspection of the airplane, the damage was not discovered at the time. When the flight instructor performed the next takeoff, he noticed that the elevator flight control was sluggish and minimally responsive, and the airplane’s climb performance was poor. The flight instructor landed the airplane without further incident. The damage was discovered during a subsequent inspection. The flight instructor reported no preaccident mechanical malfunctions or anomalies that would have affected normal operation.