On March 18, 2012, at 1738 central daylight time, a Piper PA-28R-200 airplane, N56273, was substantially damaged while landing at Houston Southwest Airport (KAXH), Arcola, Texas. The flight instructor and pilot-receiving-instruction were not injured. The airplane was registered to and operated by Dutch Wings, LLC, under the provisions of 14 Code of Federal Regulations Part 91 while on an instrument flight plan. Day visual meteorological conditions prevailed for the instructional flight that departed KAXH at 1500. The pilot-receiving-instruction reported that an application of full left rudder along with right aileron input was required to maintain alignment with the runway centerline during final approach to runway 9 (5,003 feet by 100 feet, asphalt). He stated that as the airplane crossed over the touchdown zone he reduced engine power and flared for touchdown. During the landing flare, the airplane encountered a wind gust and drifted off the left edge of the runway. He stated that his flight instructor assumed control of the airplane and attempted a go-around, but the airplane was unable to climb and subsequently landed in a ditch before sliding into a nearby hangar. The flight instructor reported that the airplane encountered a wind gust during the landing flare and began to drift left of the runway centerline. He noted that he assumed control of the airplane as it drifted off the left side of the runway. He stated that he advanced engine power for a go-around, but the airplane had insufficient airspeed to establish a climb. He further noted that the pilot-receiving-instruction did not relinquish his left rudder input, and in combination with the left-turning tendency experienced at takeoff power he was unable to reestablish directional control before the airplane impacted a ditch. The fuselage and wings were substantially damaged during the accident sequence. The flight instructor reported that there were no preimpact mechanical malfunctions or failures that would have precluded normal operation of the airplane. At 1735, the airport's automated surface observing system reported the following weather conditions: wind 130 degrees at 11 knots, gusting 15 knots; visibility 10 miles; temperature 23 degrees Celsius; dew point 20 degrees Celsius; altimeter setting 29.98 inches of mercury. The sky condition was not reported.