On March 20, 2001, at 0930 hours mountain standard time, a Piper PA-28-181, N4188E, landed short of runway 04 at the Gila Bend Municipal Airport, Gila Bend, Arizona. The airplane was operated by Sabena Airline Training Center as an instructional flight under the provisions of 14 CFR Part 91, and was substantially damaged. The certified flight instructor (CFI) and two private pilots were not injured. Visual meteorological conditions prevailed for the local area flight. The flight was originating at the time and was scheduled to terminate at the Gila Bend airport. No flight plan had been filed. Both the CFI and the student estimated the wind to be from 040 degrees, between 5-10 knots. In the CFI's written statement to the Safety Board she indicated that the pilot had made two landings prior to the accident landing with no discrepancies noted with the flight pattern or landings. On the third approach she simulated an engine failure for the student pilot. No discrepancies were noted with the approach. She noted that he made all of his target altitudes and airspeeds. She stated that at 2,100 feet he added 10 degrees, first notch, of flaps, and maintained 70 knots. She further noted that when he was established on final the airplane's altitude was 1,300 feet msl and 70 knots. The CFI believed the student was in a normal safe position to perform the power off approach. At 1,000 feet msl the student told the CFI that he didn't think he was going to make the landing. She looked at the altimeter, which read 1,100 feet, and the airspeed indicator that still read 70 knots, and told the student that they would continue the approach because this "was a real life situation." She looked at the windsock and verified that the winds were down the runway at 10 knots. The CFI selected 25-degrees of flaps, and still felt that the approach was normal. The CFI stated that the student elected to go around and added full throttle. She felt the airplane sinking rapidly in a straight and level attitude. She then saw the airspeed decreasing rapidly. She reduced the flaps to 10 degrees; however, the airplane continued to descend. The CFI reported that it appeared they had encountered wind shear, from a straight headwind to no wind at all. The airspeed continued to drop. Prior to impact the student pulled back on the yolk. The CFI noted that the airspeed was at 40 knots, with no sound emanating from the stall warning horn. In the student's written report to the Safety Board he indicated that when he turned on final he noted a stronger headwind than he was expecting, or that it had increased, and was pushing the airplane away from the runway. He voiced his concerns to the CFI, and told her that he was going to maintain the 10 degrees of flaps selected and 70 knots. He told her that he did not want to increase the drag with 25 degrees of flaps. On short final the student estimated the distance to the runway, with the altitude he was at, to be longer than what would be necessary to land on the runway. He informed the CFI that he was going to go around. His flight instructor told him to proceed with the landing, and then the CFI selected 25 degrees of flaps. The pilot adjusted his airspeed to compensate for the increased drag and noted that the airspeed was now at 65 knots. He noted the loss of altitude and called out that he was going around. He simultaneously advanced the throttle to full forward and kept a level attitude with the horizon. The pilot stated that he saw the airspeed drop below 50 knots and that the airplane was sinking towards the ground. He stated that the airplane crashed into some desert brush and came to an immediate full stop in a ditch. There were no discrepancies noted with the airplane or engine by either pilot.