THE INSTRUCTOR REPORTED THAT HE INITIATED A SIM ENGINE FAILURE DURING CLIMB AT ABOUT 100 FT AGL, AS PART OF THE RECURRENCY FLIGHT. THE PILOT INITIATED AN AUTOROTATION, AT ABOUT 50 FT AGL, THE RATE OF DESCENT INCREASED AND THE THROTTLE WAS ROLLED IN TO ARREST THE DESCENT. ACCORDING TO THE CHECK PLT, THE ENGINE FAILED TO RESPOND, AND A FLARE WAS INITIATED IN AN ATTEMPT TO SLOW THE HELO. THE HELO SUBSEQUENTLY IMPACTED THE TERRAIN IN A TAIL-LOW ATTITUDE AND ROLLED OVER. THE PVT PLT NOTED THAT HE & THE INSTRUCTOR HAD PERFORMED 3 PRIOR SIM ENGINE FAILURES SHORTLY BEFORE, AND HAD EXECUTED A POWERED RECOVERY TO A HOVER AFTER EACH MANEUVER. EXAM OF THE HELO REVEALED NO EVIDENCE OF PRE-EXISTING MECHANICAL MALFUNCTION OR FAILURE. THE FUEL-INJECTED ENGINE STARTED AND RAN NORMAL AFTER 3-4 START ATTEMPTS, AND RESPONDED TO THROTTLE INPUTS IN A NORMAL MANNER.