B757 FLT CREW EXPERIENCES TE FLAP DISAGREE EICAS MESSAGE DURING APPROACH AFTER PREVIOUS WRITE-UP FOR THIS PROBLEM WAS SIGNED OFF AS 'COULD NOT DUPLICATE' BY MAINTENANCE.

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REPETITION OF PREVIOUS DISCREPANCY: TRAILING EDGE FLAP DISAGREEMENT. YESTERDAY'S GRIPE SIGNED OFF CYCLED FLAPS -- UNABLE TO DUPLICATE. ON FINAL APCH AFTER FLAPS 20 DEGS (WITH GEAR UP) WAS SELECTED AND TRAILING EDGE FLAP DISAGREEMENT EICAS MESSAGE ILLUMINATED. TRAILING EDGE FLAPS LOCKED OUT AT APPROX 16 DEGS. EXECUTED MISSED APCH. REQUESTED AND RECEIVED VECTORS AND A CLB TO 5000 FT. COMPLETED APPROPRIATE NORMAL AND ABNORMAL CHKLISTS. ADVISED TRACON THAT WE WOULD NOT REQUIRE EMER EQUIP WHEN WE RETURNED FOR LNDG. REQUESTED RWY 28 AND EXPLAINED THAT WE WOULD BE CONFIGURING EARLY AND TO EXPECT NO MORE THAN 150 KTS AT THE OM. ADVISED FLT ATTENDANTS OF CONDITION AND EXPECTED LNDG TIME. SENT MESSAGE TO DISPATCH IDENTING EICAS MESSAGE. TOLD THEM WE WOULD BE LNDG AND INSTRUCTED THEM TO ADVISE MAINT OF SIT. MADE PA ANNOUNCEMENT TO PAX EXPLAINING SIT AND PLAN FOR LNDG WITH LESS FLAPS THAN NORMAL. AFTER FINISHING ROUTINE AND ABNORMAL CHKLISTS AND OBTAINING LNDG DISTANCE DATA FROM IRREGULAR CONFIGN LNDG DATA TABLE; WE COMPLETED AN APCH AND LNDG ON RWY 28. USING FLAPS 20 DEGS; AUTOBRAKES 3 DEGS AND NORMAL REVERSE; AIRPLANE WAS BROUGHT TO AN APPROPRIATE SPD FOR EXIT AT TXWY T. WE DID NOT RECONFIGURE AFTER LNDG. TAXIED TO GATE WITH FLAPS AND SLATS EXTENDED.