The flight instructor reported that he and the student pilot were conducting touch-and-go landings. As the pilot turned from base to final, a “fairly significant crosswind” that had shifted while they were in the traffic pattern pushed the airplane left of the runway centerline. After realigning the airplane with the extended runway centerline, right aileron and “nearly full left rudder deflection” were required to stay on course. When the airplane was on short final, about 200 ft agl, it encountered windshear and descended rapidly, impacting the ground about 200 ft short of the runway threshold. The airplane sustained substantial damage to the engine mounts. The pilots reported that there were no preaccident mechanical malfunctions with the airplane that would have precluded normal operation. The flight instructor reported that he took control of the airplane to initiate a go-around but was unable to arrest the descent before ground impact. About the time of the accident, the student pilot was landing on runway 31 with wind from 360o at 9 knots.