INST INSTRUCTOR FAIL TO CANCEL IFR FLT PLAN AT NON TWR ARPT.

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I DEPARTED HPN ON AN IFR FLT PLAN TO OXC A NON-TWRED ARPT. THIS WAS AN INST TRAINING FLT CONDUCTED IN VFR CONDITIONS; LASTING ABOUT TWENTY MINS TO A HALF-HR. I ASKED FOR HOLDING BEFORE THE APCH BUT THE CTLR WAS TOO BUSY; AND WE TOOK VECTORS TO THE FINAL APCH COURSE. LATER; WHEN VECTORED ONTO FINAL; THE CTLR GAVE US THE OPTION OF SWITCHING TO THE UNICOM FREQ OR TO REMAIN WITH HIM NOTING THAT HE WOULD BE ABLE TO HEAR US TO THE GND. I CHOSE THE UNICOM FREQ IN ORDER TO SELF-ANNOUNCE OUR POS. THE CTLR THEN SAID SOMETHING LIKE 'I'LL TALK TO YOU SOON.' WE SELF-ANNOUNCED ON THE APCH; DID A TOUCH AND GO; AND THEN SWITCHED THE TRANSPONDER FROM XXXX TO 1200. WE CLBED UP TO 4500; BUT DUE TO THE CLOUDS; WENT BACK DOWN TO 3500. AFTER THE CLB WE PRACTICED HOLDING AND HOLDING ENTRIES ABOVE ONE OF WATERBURY'S NDB'S. ON THE WAY BACK INTO HPN; WE WERE TOLD TO CALL ON LNDG. WHICH WAS AN IMMEDIATE INDICATION I HAD DONE SOMETHING WRONG (WHEN DO THEY GIVE YOU A PHONE NUMBER WHEN YOU'VE DONE SOMETHING CORRECT?) I SPOKE TO A CTLR OVER THE PHONE WHO INFORMED ME I HAD FAILED TO CLOSE MY FLT PLAN; WHICH PREVENTED OTHER PLANES FROM DOING APCHS AT OXC UNTIL I HAD CALLED NEW YORK APCH ON THE WAY BACK INTO HPN. THE OXC AIRSPACE WAS HELD OPEN FOR US FOR CLOSE TO 1 HR. ASIDE FROM THE FACT THAT I SIMPLY SHOULD HAVE REMEMBERED TO CLOSE THE PLAN; TWO OTHER THINGS CAME TO MIND. THE CTLR INFORMING ME THAT 135.10 COULD BE RECEIVED BY NY DOWN TO THE GND AND HIS COMMENT 'I'LL TALK TO YOU SOON' SHOULD HAVE REMINDED ME OF WHAT I HAD TO DO.