THE INSTRUCTIONAL FLT HAD BEEN IN THE AIR FOR ABOUT 45 MIN WHEN THE INSTRUCTOR TOLD THE PLT TO RETURN TO THE ARPT AND LAND. UPON ENTERING THE TRAFFIC PATTERN THE PLT WAS TOLD TO MAKE A TOUCH AND GO LANDING. HE COMPLETED TWO OF THESE MANEUVERS AND WAS ATTEMPTING THE THIRD TAKEOFF WHEN THERE WAS A REPORTED LOSS OF POWER ON THE LEFT ENG. THE ACFT WAS AIRBORNE AT THE TIME AND TURNED LEFT. THE INSTRUCTOR GOT ON THE CONTROLS AND TURNED BACK TO THE RWY HEADING WHICH PUT THEM OVER A SOD STRIP PARALLEL TO THE ORIGINAL RWY. HE RAISED THE LANDING GEAR AND THE ACFT STARTED A SLOW CLIMB THEN STARTED SETTLING TOWARD THE GROUND. HE SAW THE OBSTRUCTIONS AHEAD AND MOVED THE THROTTLE AND PROP LEVERS AFT. DURING THE ATTEMPTED OFF AIRPORT LANDING THE LEFT WING CONTACTED THE GROUND AND THE ACFT CARTWHEELED. NEITHER OF THE PILOTS FEATHERED THE ENG WHICH PRODUCED THE POWER DIFFERENTIAL. CAUSE OF THE REPORTED POWER LOSS WAS NOT DETERMINED.