A B737-300 THAT WAS DISPATCHED WITH ONE BLEED INOP EXPERIENCED A LOSS OF CABIN PRESSURE. THE FLT CREW EXECUTED AN EMERGENCY DESCENT AND CONTINUED TO DESTINATION WITHOUT DECLARING AN EMERGENCY WITH ATC.

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ACFT WAS ON AN MEL FOR #1 BLEED TURNED OFF. PROC TO FLY BELOW FL250; SINGLE PACK; ISOLATION VALVE CLOSED. FIRST LEG ACFT OPERATED NORMALLY. DURING SECOND LEG AT FL240 WITH CRUISE PWR; PRESSURE WARNING HORN SOUNDED. I WAS THE PLT MONITORING AND TOLD ATC WE NEEDED LOWER AND BEGAN PUTTING ON MY MASK. I ALSO ENSURED THE FO WAS DOING THE SAME. CTR STATED NEW SQUAWK AND EXPECT DSCNT MOMENTARILY. I WAS FINISHING PUTTING ON MY MASK AND STATED; 'WE NEED LOWER NOW; PRESSURIZATION.' WE WERE GIVEN 14000 FT AND BEGAN OUR DSCNT. I WAS USING THE QRH AS THE FO WAS FLYING WHILE I ATTEMPTED TO REGAIN PRESSURIZATION. THE CABIN ALT REACHED 15000 FT AND I HEARD THE FLT ATTENDANTS INFORMING THE PAX ABOUT USE OF THEIR MASKS. I WAS UNABLE TO REGAIN CABIN PRESSURE AND REQUESTED 10000 FT. WE LEVELED OFF AT 10000 FT AND FINISHED THE LOSS OF CABIN PRESSURE AND RAPID DSCNT CHKLISTS. I REMOVED OUR MASKS AND TALKED TO THE FLT ATTENDANTS; PAX; AND CONTACTED DISPATCH. ALL PAX WERE OK; SO I ELECTED TO CONTINUE. I DID NOT DECLARE AN EMER NOR DID I DEVIATE FROM ANY ASSIGNED ALTS. CTR DID ASK FOR SOB; FUEL; AND INTENTIONS; AND I ELECTED TO TERMINATE THE EMER. RECOVERY WAS NORMAL. I SHOULD HAVE DECLARED AN EMER TO PREVENT ANY CONFUSION; AND BEEN QUICKER NOTIFYING THE FLT ATTENDANTS.