On August 11, 2001, approximately 1215 central daylight time, a Schweizer 269C-1 helicopter, N1234X, registered to and operated by Stinson Air Center of San Antonio, Texas, was substantially damaged during a hard landing at the Stinson Municipal Airport, San Antonio, Texas. The certified flight instructor (CFI) and his student pilot were not injured. Visual meteorological conditions prevailed and a flight plan was not filed for the 14 Code of Federal Regulations Part 91 instructional flight. The local flight originated at 1130. About 45 minutes into the flight, the CFI demonstrated a power recovery autorotation. He then allowed the student to perform the maneuver. The CFI informed the student that he "would be near the flight controls" and he would advise the student on corrective actions to take during the practice autorotation. Following the the entry into the autorotation, the CFI checked that the engine and rotor RPMs appeared to be normal. At approximately 10-15 feet agl, the CFI instructed the student to apply engine power. The engine power did not respond to throttle movement so the CFI took the controls, and it appeared that the engine had "failed." The helicopter then landed "hard" and turned 180-degrees, resulting in structural damage to the fuselage and tail boom. The reason for the loss of engine power was not determined.