DC9-30 HAS TO MAKE A RAPID DSCNT DUE TO DIFFICULTY IN MAINTAINING CABIN PRESSURE WHILE AT FL350. OK AT FL280 WITH PWR KEPT UP. CREATED SOME PROB FOR THE FLC'S APCH INTO MEMPHIS. POSTFLT FOUND A LOOSE AIR CONDITIONING BLEED DUCT LINE.

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ACFT HAD HISTORY OF PRESSURIZATION PROBS GOING BACK SEVERAL DAYS. ON CLBOUT WE FOUND THAT THE R PACK BEGAN TO CYCLE ON AND OFF. AT CRUISE WE ALSO FOUND THAT WE HAD NO CTL OF THE R TEMP CTL VALVE EITHER IN MANUAL OR AUTO. WE CALLED MAINT CTL ON THE RADIO TELLING THEM THAT WE WOULD BE SQUAWKING THE ACFT IN MEMPHIS AND DESCRIBING THE EXACT SYMPTOMS. THE CABIN ALT WAS FLUCTUATING SLIGHTLY AT THIS POINT BUT WAS HOLDING A 7500-8000 FT CABIN ALT. SHORTLY AFTER THIS; THE CABIN BEGAN CLBING AT 1000-1500 FPM AND ALL OUR ATTEMPTS TO CTL IT WERE IN VAIN. WE CALLED ZID AND REQUESTED LOWER ALT IMMEDIATELY AND STARTED A FAIRLY RAPID DSCNT AT THAT TIME WITH THEIR CONSENT. WE WERE GIVEN FL330 INITIALLY BUT TOLD THEM WE NEEDED LOWER AND TOOK A VECTOR OFF COURSE TO GO DOWN TO FL280 WHERE WE WERE ABLE TO CTL THE CABIN AGAIN. DURING DSCNT TO MEM ARPT WE NEEDED TO KEEP 1.6 EPR ON BOTH ENGS TO KEEP CABIN COMING DOWN AND TOOK SEVERAL VECTORS TO ENABLE US TO KEEP PWR AND SPD UP. MECHS FOUND BLEED DUCT PIPE FREE AND FLOPPING AROUND CAUSING INTERMITTENT LOSS OF AIR TO PRESSURE REGULATOR VALVE WHICH CAUSED VALVE TO OPEN AND CLOSE.