MAUI TWR CTLR IS CONCERNED ABOUT AN ACFT ON A MAUI POS SYMBOL OBSERVED DSNDING OVERHEAD MAUI THEN DISAPPEARS.

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WHILE WORKING LCL CTL; I OBSERVED AN ACFT 10 MI NW OF MAUI ATCT. THE ACFT WAS AT 9300 FT DSNDING OVER THE W MAUI MOUNTAINS (ELEVATION 5788 FT). I CALLED MAUI APCH AT HNL CERAP TO QUERY IF THIS ACFT WAS INBOUND TO MAUI SINCE IT WAS ON OUR CTL SYMBOL; DSNDING INTO HIGH TERRAIN AND HDG AWAY FROM THE ARPT. APCH INFORMED ME THAT THEY WEREN'T TALKING TO HIM BUT; A CTR SECTOR WAS AND THE ACFT WAS BOUND FOR ANOTHER HAWAIIAN ISLAND. THE ACFT HAD DISAPPEARED FROM THE RADAR SCOPE. THE LOA BTWN HNL CERAP AND MAUI ATCT ALLOWS THE XFER OF RADAR IDENT TO BE MADE THROUGH THE USE OF THE MODIFY/QUICK LOOK FUNCTION. HOWEVER THIS RECURRING PROB OF ACFT OVERFLTS EITHER ALLOWED TO OR THROUGH A SOFTWARE PROB CHANGING TO MAUI ATCT'S CTL SYMBOL (WITH XFER OF RADAR IDENT) IS POTENTIALLY A DISASTER WAITING TO HAPPEN. THESE OVERFLTS ARE WELL CLR OF MAUI ATCT'S AIRSPACE. SOMETIME AFTER RADAR WAS LOST WITH ACFT; THE CTR CALLED TO ASK IF WE HAD THE TAG. THE CAB COORDINATOR INFORMED THEM THAT IT MIGHT HAVE BEEN INADVERTENTLY DROPPED FROM THE COAST LIST AT MAUI ATCT. ADDITIONALLY WITH THE DATA TAG ON MAUI ATCT'S CTL SYMBOL LOW ALT AND CONFLICT ALERTS WILL BE SENT TO MAUI ATCT RATHER THAN THE CTR SECTOR ACTUALLY RESPONSIBLE FOR THE ACFT.