The pilot reported he was cruising at 300 feet over sand dunes when there was a loud bang, accompanied by a sudden loss of engine power. He immediately lowered the nose to maintain 40 knots and selected the only suitable landing area, which had a downwind component of about seven knots. Touchdown was normal but, during the landing roll, the nosewheel dug into soft sand causing the nose to drop and the gyrocopter to roll to the left, allowing the rotor to strike the ground. Examination of the two cylinder engine revealed that a stud holding the rocker gear to one cylinder head had failed, liberating the rocker gear to that cylinder. The engine manufacturer has indicated that the stud was an early design that has since been modified to eliminate the problem.