The flight instructor was providing training to the pilot for a tailwheel endorsement in the vintage military training airplane. The pilots described that it was "windy," with the wind generally aligned with the landing runway. Following several uneventful approaches and landings, the pilot was having difficulty controlling the airplane due to the wind, and the flight instructor offered to take control of the airplane and demonstrate a stabilized approach. When the airplane reached about 50 feet above the runway, the wind velocity suddenly decreased and the airplane began descending rapidly. The flight instructor responded by increasing engine power in an attempt to abort the landing; however, the airplane struck the runway and bounced back into the air. The flight instructor then completed an uneventful circuit around the traffic pattern, landed, and returned to the parking area to inspect the airplane for damage. Finding none, the pilot then restarted the airplane and flew another two circuits around the traffic pattern uneventfully. After the pilot returned to the parking area, the flight instructor noted substantial damage to the lower portion of both wings. The pilots reported that there were no mechanical malfunctions or failures of the airplane that would have precluded normal operation.