The 645-hour flight instructor was providing flight instruction to a 173-hour private pilot as part of his training towards a commercial pilot certificate. During their third landing, while practicing take offs and landings on runway 35, the pilot receiving instruction started to lose directional control of the single-engine airplane while attempting to land the nose-wheel equipped airplane with a prevailing crosswind. The instructor immediately and repeatedly told the pilot receiving instruction to abort the landing and initiate a go-around. The flight instructor reported that while attempting to initiate a go-around, the pilot receiving instruction inadvertently retracted the landing gear instead of retracting the flaps. The airplane subsequently settled hard onto the runway, coming to an abrupt stop on the runway. The winds at the time of the mishap were reported by the flight instructor to be from the northwest at 15 knots, gusting to 19 knots. Runway 35 was reported to be 4,004-feet long, by 60-feet wide. Examination of the airplane revealed structural damage to the lower bulkhead.