C340 PLT DURING INST TRAINING HAS GEAR COLLAPSE ON LNDG ROLL WHEN FLAPS RETRACTED. GEAR HANDLE IN DOWN POS; GEAR UP.

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PERFORMED A VOR APCH TO RWY 16. TUNED IN AWOS; WIND 50 DEGS AT 9 KTS. DECIDED TO CIRCLE APCH TO RWY 12; LNDG UNEVENTFUL ON ROLLOUT APPROX 4500 FT DOWN THE 5935 FT RWY. I RAISED THE FLAPS; OUR GND SPD WAS ABOUT 30 MPH. APPROX 3-4 SECONDS AFTER RAISING FLAPS; THE LNDG GEAR STARTED TO RETRACT; PAX SIDE FIRST. FROM WHERE THE R WINGTIP TOUCHED THE RWY TILL THE PLANE CAME TO REST WAS ONLY ABOUT 100 FT. THE AIRPLANE NEVER LEFT THE RWY. WHEN THE AIRPLANE CAME TO REST; I TURNED OFF THE FUEL; MAGNETOS; AND MASTER SWITCH. MY FRIEND AND I IMMEDIATELY EXITED THE PLANE. INJURIES NONE; NOT EVEN A SCRATCH. WHEN WE RETURNED TO THE PLANE ABOUT AN HR LATER TO RETRIEVE OUR FLT BAGS AND PERSONAL ITEMS; IT WAS NOTICED THAT THE GEAR LEVER WAS IN THE DOWN POS. WE HAVE NO IDEA WHY THE GEAR RETRACTED. THERE WAS NEVER A GEAR HORN WARNING. THE THROTTLES WERE IN THE IDLE POS; THE SQUAT SWITCHES APPARENTLY DID NOT WORK EITHER. AIRPLANE SETTLED VERY SLOWLY ON THE RWY WITH ALL GEAR TUCKED AWAY IN THE RETRACTED POS. WITH THE PLANE SITTING ON THE RWY THERE DOESN'T SEEM TO BE ANY MAJOR DAMAGE. NOTE: THIS ACFT HAD GONE THROUGH A VERY EXTENSIVE ANNUAL; WITH BOTH ENGS; PROPS; TURBOCHARGERS; WASTE GATES AND CTLRS EITHER REBUILT OR EXCHANGED ABOUT 2 MONTHS AGO; AIRPLANE HAS 37 HRS WITH 27 LNDGS SINCE ANNUAL. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATES HE NEVER DID FIND THE EXACT CAUSE OF THE GEAR COLLAPSE. THE ACFT HAS BEEN REPAIRED AND IS FLYING AGAIN. THE LCL FAA INSPECTOR CALLED THE 2 PLTS IN AND DECIDED; SINCE THEY WERE IN THE WINGS PROGRAM; THEY WERE PROFICIENT AND CONSIDERED THEIR MEETING TO BE THE END OF THE INCIDENT. RPTR CALLED THE FSS IMMEDIATELY AFTER THE INCIDENT TO NOTAM THE ARPT CLOSED UNTIL THE ACFT WAS REMOVED FROM THE RWY. RPTR HAD THE MAINT PERSONNEL CHK THE ACFT AND IT WAS FLOWN OUT FOR REPAIRS. THE BELLY WAS SCRAPED AND THE ENTIRE GEAR WAS REPLACED. PROPS WERE REPLACED. THE GEAR WARNING HORN DID NOT WORK UNLESS THE FLAPS WERE DOWN AND RPTR WAS AWARE OF THAT. HE DID NOT KNOW THAT IT WAS NOT WORKING RELATIVE TO THROTTLE POS. HOWEVER; SINCE THE HANDLE WAS DOWN IT IS STILL A MYSTERY WHY THE GEAR DID NOT EXTEND.