During the student pilot’s second instructional flight, he performed an uneventful touch and go landing. When the student was on final for his second touch and go landing, about 25 ft above the runway, he initiated an early flare and pitched the airplane down which led to a sharp descent toward the runway. The airplane landed hard and bounced on the runway. The flight instructor took the controls and initiated a go-around. The flight instructor assisted the student on one more touch and go landing, then made a full stop landing. During a post-flight inspection, substantial damage (buckling) was found on the underside of the empennage and the firewall. The flight instructor reported that the accident could have been prevented by initiating a go around earlier. No mechanical malfunctions or failures with the airplane were reported.