A B757-200'S AC PACK FAILED AT FL400 WITH PREVIOUS PRESSURE CONTROLLER PROBS. UNABLE TO MAINTAIN THE CABIN AN EMER WAS DECLARED. THE CREW LANDED AT A NEARBY ARPT.

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THE ACFT HAD A HISTORY OF PRESSURIZATION PROBS IN THE PREVIOUS 4 DAYS OF FLYING. WE HAD TAKEN THE JET FROM ZZZ TO ZZZ1 THE NIGHT BEFORE AND #2 AUTO CONTROLLER HAD BEEN DEFERRED. ALL WAS NORMAL TO ZZZ2 THE NIGHT BEFORE. WE WERE ASSIGNED THE SAME JET THE NEXT MORNING FOR THE LEG BACK TO ZZZ. MAINT HAD WORKED ON THE JET THAT NIGHT AND HAD CHANGED OUT THE #2 CONTROLLER. PASSING FL385 TO FL400; THE L PACK FAILED. FO GOT PROC OUT FOR L PACK FAILURE AND L TEMP FAILURE. I WAS WATCHING THE CABIN VSI AND IT WAS CONTINUING TO CLB AND CABIN PRESSURE WAS NOW CLBING THROUGH 8000 FT. I ASKED ATC FOR AN INITIAL ALT OF FL320 TO SEE IF WE COULD REGAIN THE L PACK AND TO SEE IF THE R PACK MIGHT BE ABLE TO KEEP THE CABIN. IT BECAME VERY APPARENT THAT NEITHER WAS GOING TO BE CTLED AS THE CABIN WAS CLBING AT 1000 FPM. WE DONNED OUR OXYGEN AND ASKED FOR DSCNT TO 10000 FT ASAP. WE TURNED ON THE SEATBELT SIGN AND FO; WHO DID A SUPERB JOB THROUGHOUT; FLEW US TO 10000 FT. I RAN THE QRC AND THEN RAN THE ITEMS IN THE FLT MANUAL. LEVEL AT 10000 FT; CHKED ON FLT ATTENDANTS AND PAX -- ALL FINE -- AND CONTACTED DISPATCH WHO ALSO WAS ON HER GAME THAT DAY AND DID A GREAT JOB; AND WE DISCUSSED THE OP OF ZZZ3 TO MAKE SURE THAT THERE WERE NO PROBS WITH US LNDG THE JET THERE. ENRTE TO ZZZ3 HAD THE CHANCE TO SPEAK TO MAINT WHO WAS ALSO VERY HELPFUL AND HAD A GREAT UNDERSTANDING OF WHAT THE CAUSE MIGHT BE. LANDED AND TAXIED WITHOUT FURTHER PROBS. WE BEAT THE MASKS. HIGHEST CABIN ALT NOTED WAS 13200 FT. NO ILL EFFECTS WERE FELT BY EITHER CREW MEMBERS OR PAX; THAT WE KNOW OF.