A PA34 L ENG STOPPED RUNNING WITH INSTRUCTOR AND STUDENT ON BOARD. EMER DECLARED AND SAFE OFF ARPT LNDG MADE.

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TRAINING FLT BEGAN A LITTLE AFTER XA30 ON MAR/FRI/05. RUNUP AND PREFLT THOROUGH; AS THE STUDENT IS NEW TO THE ACFT. WT AND BAL AND PERFORMANCE CHARTS DISCUSSED. EMER BRIEFING PERFORMED. STUDENT WAS THE SOLE MANIPULATOR OF THE CTLS UNTIL THE TIME OF THE EMER. PRACTICED STEEP TURNS; SLOW FLT AND STALLS AT ABOUT 7000-8000 FT MSL IN THE LCL PRACTICE AREA. ALSO PRACTICED 2 EMER DSCNTS. ABOUT XB15 RETURNED TO ZZZ1 ARPT TO LAND. INSTRUCTED STUDENT TO PERFORM A GAR AT ABOUT 200-300 FT AGL. BROUGHT GEAR AND FLAPS UP; BUT LEFT PROPS FULL FORWARD DURING THE 4 MI FLT TO DOWNWIND FOR RWY 30 AT ZZZ2 ARPT. RADIO CALLS RPTED A GYROCOPTER READY TO TAKE OFF RWY 30 AND ANOTHER ACFT DOING A RUNUP FOR RWY 12. STUDENT STARTED DOWNWIND CHKLIST: FUEL PUMPS ON; GEAR DOWN AND LOCKED. AT THIS POINT; PLANE STARTED TO LOSE ALT AND HDG. THE STUDENT SAID; 'SOMETHING IS WRONG.' I LOOKED AT THE GAUGES QUICKLY AND OIL TEMPS AND PRESSURES WERE GREEN. WE EXCHANGED CTLS AND I INSTINCTIVELY PULLED BACK AND WE SLOWED DOWN SOME TO ABOUT 90 KTS. THE STUDENT SAID; 'YOU ARE SLOW.' I PITCHED THE ACFT FORWARD AND APPLIED L RUDDER TO CORRECT BANK TO THE R AND ACHIEVE VYSE. I ESTIMATE WE LOST 30-40 DEGS OF HDG TO THE R AND 500 FT OF ALT. I MADE DECISION TO TURN INTO THE DEAD ENG TOWARD FIELDS INSTEAD OF TO THE L TOWARD THE TOWN AND RWY WE HAD BEEN APCHING. STUDENT TOLD ME LATER; I PUT THE QUADRANT FULL FORWARD AND VERBALLY CONFIRMED. I DO NOT REMEMBER THIS. I DO REMEMBER VERIFYING DEAD ENG AND FEATHERING THE PROP. I REMEMBER THINKING ABOUT 'RAISE THE DEAD' BUT I AM NOT SURE I DID IT. I KEPT MY EYES OUTSIDE. MY STUDENT WAS IMMEASURABLY HELPFUL AS HE KEPT AN EYE ON THE AIRSPD 105 MPH. WE IDENTED A FIELD TO LAND ON AND CLRED PWR LINES; TREES; AND A CONCRETE IRRIGATION DITCH TO LAND FACING NW ON A 1250 FT WINTER WHEAT FIELD. TIME FROM ENG FAILURE TO LNDG WAS 2-3 MINS. I CALLED 'MAYDAY; ACFT X IS GOING DOWN 1 MI W OF ZZZ2' SHORTLY BEFORE LNDG. THE LNDG WAS SMOOTH AND THE PLANE; THE STUDENT; AND I WERE UNDAMAGED AND NOT INJURED IN ANY WAY. WE MADE A RADIO CALL THAT WE WERE OK; TURNED OFF THE ACFT CTLS AND EXITED THE ACFT. ELT DID NOT GO OFF. DAMAGE TO FIELD WAS NEGLIGIBLE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: A PA34 AT FULL PWR ON A STANDARD DAY AT 5200 FT WILL MAINTAIN ALT. THEY WERE AT 5500 FT AND COULD NOT MAKE THIS OLDER ACFT FLY. THERE WAS NO CAUSE FOUND FOR THE ENG QUITTING; BUT THE RPTR DID NOT AGREE WITH THE MOST COMMONLY HELD THEORY THAT THE ENG FUEL MIXTURE WAS TOO LEAN. THEY HAD FULL RICH DURING THE ATTEMPTED RECOVERY AND THE ENG WOULD NOT RUN. THE ACFT WAS NOT DAMAGED. SUPPLEMENTAL INFO FROM ACN 651474: POSSIBLE REASON FOR THE PROB WITH THE R ENG WAS THAT THE MIXTURE WAS SET TOO LEAN. IT WAS NO PROB TRYING TO LAND AT THE ZZZ1 ARPT WITH THE SAME AMOUNT OF MIXTURE; BUT IT WAS A PROB AT ZZZ2. WE ALSO DID NOT MAKE A DECISION TO LAND AT THE ZZZ2 ARPT BECAUSE OF OTHER AIRPLANES IN THE TFC PATTERN. 1 ON THE RWY; 3 IN THE PATTERN; 1 ON THE OTHER SIDE OF THE RWY AT ZZZ2. AFTER LNDG; BOTH ENGS WERE RESTARTED AND BOTH WORKED WITHOUT ANY PROBS SO IT WAS MOST LIKELY THAT MIXTURE WAS NOT SET AND IT WAS TOO LEAN. NO OTHER FACTORS AFFECTED THE FLT OR PERFORMANCE OF THE ACFT.