NON ADHERENCE TO ATC CLRNC INSTRUCTION AFTER EXPERIENCING AN ACFT EQUIP PROB.

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WHILE APCHING NASSAU; BAHAMAS; IFR FLT PLAN FROM MIAMI IN VFR CONDITIONS; WE CONTACTED NASSAU APCH AND WE WERE TOLD TO DSND TO 4000 FT AND RPT PRUNE INTXN; 30 MI NW OF NASSAU VOR. NASSAU RADAR ON THIS PARTICULAR DAY WAS OTS. I (THE COPLT) WAS WORKING THE RADIOS WHILE THE CAPT WAS FLYING. I RPTED PRUNE INTXN. NASSAU ACKNOWLEDGED AND TOLD US TO ORBIT OVER PRUNE AND LEAVE PRUNE ON A 095 DEG HDG FOR SPACING. RIGHT OVER PRUNE WE LOST THE DME FROM NAS AND THE CAPT FAILED TO ORBIT AS WE WERE INSTRUCTED. INSTEAD WITH THE CONFUSION OF TRYING TO GET THE DME BACK; THE CAPT CONTINUED INBOUND TO NASSAU. WE PICKED UP THE DME AGAIN AND WERE SHOWING 23 DME FROM NAS. NASSAU APCH CALLED US BACK AND ASKED US THE DME. I REPLIED 23. NASSAU APCH GOT VERY UPSET WITH US AND GAVE US A HOLDING. WE WERE LATER CLRED FOR A VOR/DME APCH RWY 14 AND LANDED WITHOUT FURTHER PROB; BUT WITH THE DME INTERMITTENT. ONCE ON THE GND; THE CAPT WAS LECTURED BY THE TWR SUPVR. ALSO; WOULD LIKE TO POINT OUT THAT WHEN WE LOST THE DME OVER PRUNE; WE NEVER RPTED IT TO NASSAU AS WE SHOULD HAVE.