The flight departed the airport on a local instructional flight. When the flight returned to the airport, the CFI instructed the noncertificated student pilot to execute a simulated engine out autorotation. The student pilot entered the autorotation at a low main rotor RPM, but during the descent the RPM increased to the low side of its normal operating range. The CFI attempted to terminate the autorotation at 200 feet AGL because of the marginal low rotor RPM, but when he applied rapid full throttle the engine faltered and then failed. The CFI executed an emergency autorotative landing. On touchdown, the helicopter bounced, the skids dug into the soft dirt on the second touchdown, and the helicopter came to an abrupt stop and rolled over. The post accident engine examination disclosed that the engine operated normally throughout its normal operational parameters but when the throttle was rapidly applied after a prolonged idle the engine faltered. The idle RPM was marginal and the carburetor had recently been replaced.