A PA44 INSTRUCTOR REPORTS THAT AFTER A TOUCH AND GO LNDG THE LNDG GEAR WAS RAISED WHILE ON THE RWY CAUSING R MLG TO RETRACT.

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THE STUDENT PLT AND I DEPARTED FROM ZZZ ON A SIMULATED XCOUNTRY FLT. I GAVE THE STUDENT PLT A DIVERSION TO ZZZ1. 10 MI OUTSIDE OF ZZZ1 WE DID COMMERCIAL MULTI-MANEUVERS AND THEN I ASKED THE STUDENT TO TAKE ME TO ZZZ1 FOR A SHORT-FIELD LNDG. WE BEGAN MAKING RADIO CALLS 10 MI OUT. AFTER ENTERING A 2-3 MI L BASE FOR RWY 4; THE STUDENT LOWERED THE LNDG GEAR AND THEN PUT IN 10 DEGS LF FLAPS; THEN 25 DEGS. THE STUDENT THEN ANNOUNCED A L BASE FOR RWY 4 ON THE CTAF AND ALSO THE BASE TURN TO FINAL. AFTER TURNING FINAL; THE STUDENT DID THE BEFORE LNDG CHKLIST. ON SHORT FINAL; I VERIFIED 3 GREEN AND 1 IN THE MIRROR. I HAD PREVIOUSLY ASKED THE STUDENT TO LAND THE ACFT ABEAM THE FIRST TXWY. WE LANDED A LITTLE BEYOND COMMERCIAL STANDARDS AT AROUND 60-65 KIAS. AFTER VERIFYING THAT THE STUDENT HAD THE ACFT UNDER CTL; I RAISED THE FLAPS; KEEPING MY EYE ON THE RWY AS I DID. THEN I ASKED THE STUDENT TO CONTINUE. I DO NOT RECALL SEEING THE STUDENT'S HAND LEAVE THE THROTTLES. AS WE WERE ROLLING; THE R SIDE OF THE AIRPLANE DROPPED AND WE BEGAN TO GO TOWARDS THE L SIDE OF THE RWY. I ASKED FOR THE CTLS; NOT FULLY REALIZING WHAT WAS GOING ON. THERE WAS NOTHING I COULD DO TO KEEP THE AIRPLANE ON THE RWY. IT WASN'T UNTIL WE HIT THE RAISED GND AND I SAW THE PROP STOP WITH ITS TIP BENT THAT I REALIZED WE HAD LOST OUR R GEAR. WE ENDED UP ON AN EMBANKMENT TO THE S SIDE OF THE RWY. ONCE STOPPED; THE STUDENT AND I BEGAN TO SECURE THE AIRPLANE. THAT'S WHEN I SAW THE GEAR SELECTOR SWITCH WAS IN THE 'UP' POS. AFTER DISCUSSING WITH THE STUDENT THE MATTER OF THE GEAR SELECTOR SWITCH; THE STUDENT MAINTAINED HIS HAND WAS ON THE THROTTLE THE ENTIRE TIME; AND I DO NOT REMEMBER HIM TAKING HIS HAND OFF OF THE THROTTLE. MY 'GUT FEELING' IS THAT THE SELECTOR SWITCH WAS PUT IN THE 'UP' POS AS I WAS LOWERING THE FLAPS AND LOOKING STRAIGHT AHEAD AT THE RWY. IT'S NOT OFTEN THAT YOU GET A GEAR 'FAILURE.' IF THE SWITCH WAS IN THE 'DOWN' POS AFTER WE CAME TO REST; THEN I WOULD BE CONFIDENT OF A MECHANICAL FAILURE. BUT SINCE IT WASN'T; I'M VERY SKEPTICAL. IF IT WAS A MECHANICAL FAILURE; YOU CAN BET NEXT TIME I WILL DOUBLECHK THE J-LOCKS AND MAKE SURE THE GEAR IS LOCKED COMPLETELY. IF THIS WAS NOT A MECHANICAL FAILURE; AND IS PLT ERROR; I WILL TAKE FULL RESPONSIBILITY FOR NOT KNOWING WHERE MY STUDENT'S HAND WAS THE ENTIRE TIME. THE REASON I TOOK THE FLAPS OUT WAS SO THE STUDENT'S HAND WOULD NOT HAVE TO LEAVE THE THROTTLE. AFTER MY STUDENT LANDED; WE HAD A BRIEF EXCHANGE OF WORDS. ALL I SAID WAS 'THAT WAS A LITTLE LONG' AND HE BY 1 OR 2 WORDS AND THAT WAS IT. PERHAPS THAT WAS ENOUGH TO DISTRACT HIM. I WAS VERY CONFUSED ABOUT WHAT I SHOULD HAVE DONE AFTERWARDS; BECAUSE I THOUGHT I WAS BEING SAFE. HOWEVER; AFTER TIME TO REFLECT; I FEEL THE BEST CHOICE WOULD HAVE BEEN TO REMAIN WHERE I WAS AND LET MY STUDENT HANDLE THE FLAPS SO I COULD KEEP MY EYE ON HIS EVERY MOVEMENT. I HAVE BEEN VERY SUCCESSFUL IN THE PAST ABOUT ANTICIPATING MISTAKES MY STUDENTS WOULD MAKE AND HAVE CAUGHT THE MISTAKES BEFORE THEY GOT TOO FAR. IN THIS SITUATION; I GOT CAUGHT BECAUSE I DIDN'T RECOGNIZE THE POTENTIAL PROB OF A PREMATURE GEAR RETRACTION AND WAS NOT READY FOR THE POSSIBILITY. REGARDING THE DISTR AFTER HE LANDED; I WILL SAVE ANY COMMENTS UNTIL AFTER WE ARE STOPPED COMPLETELY OR WE ARE IN A MORE SAFE PHASE OF FLT (IE; DOWNWIND). NEITHER ONE OF US WAS FATIGUED OR DISTR BY OUTSIDE 'FACTORS' THAT I RECALL. ONE THING I COULD DO IS HAVE EVERY ONE OF MY STUDENTS CALL OUT 'GEAR UP' BEFORE THEY ACTUALLY RETRACT THE GEAR. THAT COULD 'HEAD OFF' ANY POTENTIAL PROBS.