THE FLIGHT TOOK OFF AT 1210 WITH 90 GALS OF FUEL ONBOARD. AS THE PILOTS WERE PRACTICING TAKEOFFS AND LANDINGS, THE ENGINE LOST POWER. THE CFI ASSUMED CONTROL AND ATTEMPTED TO LAND IN AN AREA WEST OF THE RUNWAY, BUT WAS UNABLE TO CLEAR A FENCE. THE AIRPLANE STRUCK THE FENCE, THEN COLLIDED WITH TERRAIN. THE ENGINE AND ACCESSORIES WERE LATER FUNCTIONALLY CHECKED AND TESTED; NO DISCREPANCIES WERE FOUND.