ACFT EQUIP PROB -- PRESSURIZATION EMER DIVERSION.

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80 MI NW OF KANSAS CITY MISSOURI WE LOST CABIN PRESSURE; FOLLOWED COMPANY SOP'S -- DECLARED AN EMER -- MADE A RAPID DSCNT AND DIVERTED TO MCI -- NO INJURIES RPTED. WE WERE AT 35000 FT WHEN WE LOST PRESSURIZATION. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: PRESSURIZATION LOSS WAS DUE TO AUTO-SHUTDOWN OF AIR CONDITIONING PACKS. COMPANY ENGINEERING SAID THAT THERE HAD BEEN SIMILAR CASES IN THIS ACFT DUE TO THE WATER SEPARATOR ICING WHICH CAUSES A LACK OF AIRFLOW ACROSS THE HEAT EXCHANGER. ALSO; THE ACFT WAS IN ICING CONDITIONS AND THE WING ANTI-ICE WAS IN USE; WHICH COULD HAVE CONTRIBUTED TO THE LOW AIRFLOW. THIS ACFT AIR CONDITIONING/PRESSURIZATION DUCTING MUST BE MAINTAINED CONSTANTLY OR THEY DEVELOP AIR LEAKS WHICH AGAIN PRECIPITATE THIS TYPE OF INCIDENT. RPTR CAPT'S FIRST NOTICE OF PRESSURE. PROB WAS FEELING IT IN HIS EARS AND WHEN LOOKING AT THE RATE GAUGE; IT WAS CLBING THE CABIN AT 2500 FPM. BOTH PLTS DONNED 02 MASKS WITH NO DIFFICULTY. THE CABIN DID GO ABOVE 10000 FT BECAUSE THE WARNING LIGHT CAME ON; BUT THE PAX 02 MASKS DIDN'T DEPLOY NOR WERE THEY DEPLOYED MANUALLY. FLC MADE AN EMER DSCNT; DECLARED EMER AND DIVERTED TO KANSAS CITY. WHEN ACFT DSNDED THROUGH 16000 FT THE PACKS CAME BACK ON AND THE ACFT RE-PRESSURIZED. WARMER AIR EITHER MELTED THE ICE IN THE WATER SEPARATOR OR TURNING OFF THE WING ANTI-ICE PROVIDED IMPROVED FLOW OF BLEED AIR. ON THE GND MAINT CHANGED THE PRESSURE REGULATOR VALVE AND FLOW CTLR VALVE AND THE RPTR FERRIED THE ACFT BACK TO THE HOME BASE. BEFORE TKOF A DEADHEADING PLT IDENTED HIMSELF TO THE CAPT AND VOLUNTEERED HIS HELP IF NEEDED SO DURING THE EMER THE FLC HAD HIM COME TO THE COCKPIT AND HE PROVIDED A LOT OF AID IN THE EMER.