PA28 INSTR AND TRAINEE CHALLENGE LWM LC OVER POS RPTING AND PROX TO ARPT.

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MY INSTRUCTOR (CFII/ATP) AND I DEPARTED HANSCOM FIELD (KBED) ARPT FOR THE PURPOSES OF TRAINING. WE PROCEEDED ENRTE TO LAWRENCE (KLWM) ARPT. WE MADE A CALL TO LAWRENCE TWR FROM A DIST OF APPROX 11 NM REQUESTING TOUCH AND GOES. LAWRENCE TWR INSTRUCTED US TO REPORT A 2 MI RIGHT BASE FOR RWY 14. SHORTLY THEREAFTER; LAWRENCE TWR CALLED US; ASKING FOR OUR CURRENT POS. WE RESPONDED IMMEDIATELY; SAYING WE WERE ON A 4 MI RIGHT BASE. TWR RESPONDED; SAYING 'THANK YOU. PROCEED INBOUND.' AT APPROX 2 MI; WE CALLED LAWRENCE TWR AND REPORTED '2 MI RIGHT BASE.' THIS WAS NOT ACKNOWLEDGED BY THE TWR; AND IN HINDSIGHT; WAS THE START OF THE PROB. I NOTED TO MY INSTRUCTOR THAT THEY HAD NOT ACKNOWLEDGED; AND WE PROCEEDED INBOUND. AT THE TIME; THERE WERE PERHAPS 2 OTHER ACF IN THE GENERAL AREA; AND A FEW ON THE GND WAITING TO DEPART. WE RPTED OUR POS AGAIN; BUT STILL RECEIVED NO RESPONSE. STILL HAVING HEARD NOTHING FROM THE TWR; WE TURNED FINAL; AND I WAS JUST ABOUT TO ASK THE TWR WHETHER OR NOT WE HAD CLRNC FOR TOUCH AND GO WHEN SHE SPOKE ON THE RADIO IF THAT WAS US ON FINAL? GAR IMMEDIATELY. I TOLD YOU TO RPT A 2 MI RIGHT BASE. THIS IS A PLT DEV. WE IMMEDIATELY COMPLIED WITH THE GAR INSTRUCTION; AND MY INSTRUCTOR RESPONDED TO THE TWR SAYING THAT WE RPTED 4 MI RIGHT BASE WHEN YOU CALLED US; AND WE RPTED A 2 MI RIGHT BASE AFTER THAT. YOU WERE BUSY TALKING TO OTHER ACFT AND WE ATTEMPTED TO CALL YOU YET AGAIN; BUT IT APPEARS WE MUST HAVE BEEN STEPPED ON. WE FAILED TO RECEIVE ACKNOWLEDGEMENT FROM THE TWR WHEN WE RPTED OUR POS; THE TWR CTLR EVIDENTLY WAS UNABLE TO TRACK OUR POS AND KEEP IT IN MEMORY FOR THE LESS THAN 3 MINS IT TOOK TO GO FROM 4 MI RIGHT BASE TO FINAL; AND CLRLY WAS UNABLE TO KEEP UP WITH THE TFC FLOW (WHICH WAS EXTREMELY LOW AT THE TIME). WE ALSO FAILED TO ENSURE THAT WE RECEIVED ACKNOWLEDGEMENTS FROM THE TWR.