C172 INST TRAINING FLT CONDUCTS MISSED APCH PROC AFTER TOUCH-AND-GO LNDG FROM A VOR APCH WITHOUT FIRST CONTACTING TWR FOR DEP INSTRUCTIONS.

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WE WERE ON AN IFR TRAINING FLT. WE HAD AMENDED OUR ORIGINAL CLRNC TO ITH ARPT. WE WERE CLRED VOR 14; ITH; BY APCH AND CLRED FOR AN 'OPTION APCH' BY THE ITH TWR. AFTER EXECUTING A TOUCH-AND-GO; WE INITIATED A CLBING L TURN TO 3100 FT MSL VIA 313 DEG HDG; DIRECT ITH VOR; WHICH WAS THE PUBLISHED MISSED APCH PROC. WE ADVISED TWR WE WERE ON THE MISSED APCH. WHEN WE HAD REACHED APPROX A 090 DEG HDG CLBING THROUGH 1600 FT MSL; TWR INSTRUCTED US TO TURN R TO A 200 DEG HDG AND NOTIFIED US THAT WE SHOULD NOT HAVE FLOWN THE PUBLISHED MISSED APCH; BUT RATHER RWY HDG. WE COMPLIED WITH THE HDG ASSIGNMENT. TWR INSTRUCTED US TO CONTACT ELMIRA APCH; WHICH WE DID. WE MAINTAINED 200 DEGS AND VFR UNTIL WE FILED A NEW IFR FLT PLAN. UPON REFLECTION LATER; I REALIZED THAT ONCE THE 'WHEELS TOUCHED' AT ITH ARPT; THE IFR FLT PLAN WAS TERMINATED AND WE BECAME VFR AND RWY HDG FOR THE GAR WAS APPROPRIATE. THE PROB WAS CAUSED BY THE PIC'S FAILURE TO REALIZE THE IFR FLT PLAN HAD AUTOMATICALLY CANCELED. IT WILL BE PREVENTED IN FUTURE; BASED ON UNDERSTANDING.