B737-800 FLT CREW HAS LOSS OF PRESSURIZATION DURING CLB.

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REVIEWING THE ACFT LOGBOOK; WE WERE AWARE OF 2 PREVIOUS WRITE-UPS DESCRIBING THE PRESSURIZATION PANEL AUTO FAIL LIGHT AND ALT WINDOWS DIGITS FLICKERING; BUT PRESSURIZATION WORKING NORMALLY. BOTH WRITE-UPS WERE ADDRESSED BY MAINT AND CLRED. THE FLT FROM WAS UNEVENTFUL. WE KEPT A WATCHFUL EYE ON THE PRESSURIZATION AND CTLR; AND IT FUNCTIONED NORMALLY. OUR DEP FROM ZZZ WAS UNEVENTFUL. AGAIN; WE MONITORED THE CTLR AND CABIN ALT CAREFULLY DURING THE CLB. EVERYTHING APPEARED TO BE ON SCHEDULE UNTIL AROUND FL350. WE THEN NOTICED THAT THE CABIN WAS CLBING JUST A LITTLE BIT HIGHER THAN SCHEDULED (AROUND 8000 FT). AS WE APCHED FL370; THE PRESSURIZATION CONTROLLER ALT DIGITS AND LIGHTS BEGAN TO FLICKER AS PER THE PREVIOUS WRITE-UPS. AS WE HAD REVIEWED THE QRH PROC; WE CHKED TO SEE IF ANY OF THE EFIS-RELATED SYMPTOMS WERE EVIDENT. THEY WERE NOT. WE THEN NOTICED THE CABIN WAS BTWN 8500-9000 FT. IT BECAME APPARENT THAT THE CABIN WAS NOT GOING TO STOP CLBING; SO WE BEGAN TO ACCOMPLISH THE CHKLIST BY SELECTING THE ALT CONTROLLER WHICH HAD NO EFFECT. THE CABIN ALT CONTINUED TO RISE; WITH THE HORN SOUNDING AT 10000 FT CABIN ALT. CAPT (PLT MONITORING) DIRECTED A DSCNT; AND COORD WITH ATC; DECLARING AN EMER. WITH CLRNC; AND THE CABIN ALT AT APPROX 11000 FT; FO (PF) BEGAN THE EMER DSCNT PROC. WE DONNED OUR OXYGEN MASKS; AND STARTED DOWN TO 10000 FT MSL; AND BACK TOWARDS SHORE. WHILE DSNDING THROUGH FL270; THE CABIN ALT REACHED JUST OVER 14000 FT AND THE PAX EMER OXYGEN MASKS DEPLOYED AUTOMATICALLY. ONCE ESTABLISHED IN THE DSCNT; WE WERE ABLE TO USE MANUAL CTL TO CTL THE CABIN SOMEWHAT. THE CABIN ALT DIDN'T GET MUCH ABOVE 14000 FT -- WE ESTIMATE 14500 FT.