A B737-300 CREW HAD A CHRONIC 'STABILIZER OUT OF TRIM' FOR THE 'A' AUTOPLT. THEY HAD A 500 FT ALTDEV AS A RESULT.

Narrative

THE ACFT WAS LEVEL AT 14000 FT ON THE JAMMN 4 ARR. I; THE CAPT; WAS FLYING. THE 'A' AUTOPLT/COMMAND MODE AND LNAV WERE IN USE. I AND THE FO PULLED OUT OUR APCH AND AIRFIELD DIAGRAMS TO FURTHER DISCUSS THE LNDG AND TAXI IN AT SALT LAKE. AS I LOOKED UP FROM MY AIRFIELD DIAGRAM; I WAS SHOCKED TO SEE THE ACFT AT APPROX 13600-13500 FT AND SMOOTHLY DSNDING. THE AUTOPLT WAS STILL ENGAGED; NO DSCNT MODE WAS SELECTED AND NO AUDIO OR VISUAL ALARMS OR INDICATIONS WERE PRESENT. AS I QUICKLY RETURNED THE ACFT TO 14000 FT; I NOTICED A FLICKER OF THE STABILIZER OUT OF TRIM LIGHT. WE INFORMED ATC WE WERE HAVING AUTOPLT PROB. THE ACFT OPERATED NORMALLY ON THE 'B' AUTOPLT. WE REVIEWED THE QRH AND NOTIFIED MAINT UPON LNDG. MAINT INDICATED THE ACFT HAD A HISTORY OF 'A' AUTOPLT/STABILIZER OUT OF TRIM PROBS. THE 'A' AUTOPLT WAS THEN MEL'ED INOP. WE FLEW THE REST OF THE DAY ON 'B' AUTOPLT WITHOUT INCIDENT. THIS IS A VERY INSIDIOUS AND POTENTIALLY DANGEROUS MALFUNCTION. POSSIBLY IF THE FO AND I WERE NOT BOTH LOOKING AT THE APCH PLATE AT THE SAME TIME THE ALTDEV AND DSCNT COULD HAVE BEEN DETECTED AND CORRECTED SOONER. A HEADS UP; HEADS DOWN; CALL BTWN THE FO AND I MIGHT MINIMIZE THE CHANCE OF THIS HAPPENING AGAIN IN THE FUTURE.