A B737 FLT CREW EXPERIENCED A PRESSURIZATION PROBLEM AND DIVERTED TO THE NEAREST SUITABLE AIRPORT.

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PLANE WAS DEFERRED IN ZZZ WITH AUTO PRESSURIZATION SYS INOP DUE TO OSCILLATIONS OF OUTFLOW VALVE AND CABIN VSI. CAPT WHO FLEW PLANE TO ZZZ1 SAID PLANE WAS 'GOOD' WHEN WE MET IN CONCOURSE. WHEN I GOT TO THE PLANE WE REALIZED THAT THE AUTO PRESSURIZATION WAS DEFERRED. I DISCUSSED WITH FO THAT I WOULD NOT TAKE THIS PLANE OUT OF A MAINT BASE AND CONSIDERED REFUSING THE PLANE IN ZZZ1 DUE TO 2 HR FLT BACK OVER HIGH TERRAIN. SINCE THERE WAS NO MAINT AND STANDBY PRESSURIZATION WAS RPTED AS WORKING NORMAL; WE ACCEPTED THE PLANE. LEVELING AT FL350; FO NOTICED THE +/-300 FPM FLUX IN CABIN VSI ALONG WITH OSCILLATION OF OUTFLOW VALVE. CABIN DIFFERENTIAL WAS IN THE YELLOW RANGE. I IMMEDIATELY ASKED ATC TO DSND TO FL250 WHICH WE DID. AFTER A BRIEF DISCUSSION WITH FO; WE DECIDED THAT WE DIDN'T KNOW IF THE STANDBY SYS WOULD MAINTAIN PRESSURE AND WE DECIDED THAT A DIVERT TO ZZZ2 WOULD BE BEST. I TRIED CONTACTING DISPATCH; BUT COMPANY FREQ NEVER WORKED. I NOTIFIED DISPATCH VIA ACARS THAT WE WERE DECLARING EMER FOR PRESSURIZATION PROB; DSNDING TO LOWER ALT AND DIVERTING TO ZZZ2. WE DECIDED ZZZ2 WAS THE BEST COURSE AS WE WERE N BY 80 MI AND COULD DSND TO 12000 FT VICE CONTINUING TO ZZZ AND NOT BEING ABLE TO DSND BELOW 16000 FT. I NOTIFIED FLT ATTENDANTS AND PAX AND WE CONTINUED TO ZZZ2. AT THE GATE; THE CABIN DID NOT DEPRESSURIZE UNTIL AGENT OPENED DOOR 1L; EVEN WITH 'FLT/GRD' SWITCH IN 'GRD.' FOLLOW-UP CALL TO B737 MAINT CTLR REVEALED THAT WHEN ZZZ MAINT DEFERRED THE AUTO SYS; THEY DIDN'T DO THE APPROPRIATE ANALYSIS AND TROUBLESHOOTING OF WHY AUTO SYS WAS FLUCTUATING. MAINT MADE THE COMMENT THAT HE WAS TIRED OF SEEING A 'GET OUT OF TOWN MENTALITY' WITH REGARD TO DEFERRALS. WITH ALL OF THE PROBS WITH PRESSURIZATION ON THE B737'S; I WILL NOT ACCEPT ANOTHER PLANE ANYWHERE WITH AUTO INOP. PAX TRUST US TO GET IT RIGHT THE FIRST TIME; NOT CUT CORNERS; AND PUT SAFETY FIRST IN ALL THINGS. HAD THIS DEFERRAL BEEN FIXED IN ZZZ; EVEN WITH A DELAY; THE COST OF DIVERSION; PAX INCONVENIENCE; AND CREW REASSIGNMENT WOULD HAVE BEEN AVOIDED. THANK GOODNESS IT DIDN'T RESULT IN BENT METAL.