THE HELICOPTER INSTRUCTOR PILOT AND DUAL STUDENT WERE PRACTICING AUTOROTATIONS THAT WERE TERMINATED WITH POWER RECOVERIES AT A 3-FOOT HOVER. DURING THE SIXTH AUTOROTATIVE APPROACH THE ENGINE FAILED AND THE HELICOPTER LANDED HARD. THE HARD LANDING SUBSTANTIALLY DAMAGED THE HELICOPTER. AN ENGINE OPERATIONAL TEST AFTER THE ACCIDENT DISCLOSED THAT THE ENGINE WOULD NOT OPERATE AT IDLE RPM. THE CFI HAD LOGGED 154 TOTAL HELICOPTER FLIGHT HOURS OF WHICH 9 HOURS WERE IN THE ACCIDENT HELICOPTER MAKE AND MODEL. HE HAD ALSO GIVEN 20 HOURS OF HELICOPTER FLIGHT INSTRUCTION.