After takeoff following the third touch & go landing on RWY 36, during the downwind leg where the flight was about 1 mile west of the departure runway, the student advised the CFI that he smelled something burning & that the engine wasn't producing power. The CFI advanced & retarded the throttle & observed that the manifold pressure needle movement followed the throttle movement, then gave control of the aircraft back to the student. The student again stated that the engine wasn't producing power & the CFI took control, turned to the east to land on a taxiway, & landed hard short of the taxiway. Fuel quantity was sufficient to sustain engine operation & the fuel supply did not contain contaminants. The engine was started after the accident & operated only to 1,500 RPM due to damage to the propeller assembly. The engine was then sent to the manufacturer's facility operated with the only discrepancy noted that the fuel flow at 80 PPH was 9 PPH leaner than specification. No determination could be made as to the reason for the loss of engine power.