INSTRUCTOR WITH INST STUDENT IN A C172 MAKING AN INST APCH HAS A STUCK MIKE. THIS CREATES A PROB OF LTSS FOR THE APCH CTLR.

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I WAS FLYING BACK FROM TMB TO OPF AFTER PRACTICING NDB APCH WITH MY INST STUDENT AT TMB. WE WERE VECTORED BACK TO OPF BY MIA APCH SO WE COULD PRACTICE AN ILS APCH TO A FULL STOP AT OPF. AFTER RECEIVING A VECTOR; I DIDN'T REALIZE THAT MY MIKE WAS STUCK. AFTER ABOUT 10 MINS; I REALIZED THAT MY MIKE HAD BEEN STUCK; AND I WAS SO ADVISED BY THE CTLR. AFTER LNDG; I RECEIVED A PHONE CALL FROM MIA APCH AND I WAS ADVISED THAT THEY HAD A SYS FAILURE BECAUSE OF ME; AND THAT THEIR MINIMUM SEPARATION WAS VIOLATED BTWN 2 ACFT SINCE THEY COULDN'T CALL THEM. I WAS ALSO ADVISED THAT I WILL BE CONTACTED BY THE FAA IN THE NEXT FEW DAYS. I HAVE RPTED TO THE SCHOOL OWNER AND MECH ABOUT THE FAULTY PUSH-TO-TALK BUTTON AND IT WILL BE FIXED BEFORE THE NEXT FLT. I REALIZE THAT THIS SIT COULD HAVE CAUSED AN ACCIDENT OR INCIDENT; AND THAT I SHOULD PAY MORE ATTN; AND IF THE FREQ IS QUIET FOR TOO LONG; CHK THAT MY MIKE IS NOT STUCK; AND ALSO LOOK FOR THE XMITTER LIGHT OR INDICATOR TO VERIFY THAT WE ARE NOT XMITTING.