A B737-500 LOST CABIN PRESSURIZATION AT FL280. AN EMER WAS DECLARED; BUT OXYGEN MASKS WERE NOT USED DURING THE DSCNT TO 10000 FT.

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AT FL280; THE CABIN ALT WARNING HORN SOUNDED. THE CAPT; WHO WAS THE PF; REQUESTED A DSCNT TO 11000 FT. ARTCC GAVE US A DSCNT TO FL240; AT WHICH TIME THE CAPT REFUSED AND AGAIN REQUESTED 10000 FT AND DECLARED AN EMER. ARTCC GAVE US A DSCNT TO 11000 FT FOLLOWED SHORTLY BY A DSCNT TO 10000 FT. I REQUESTED TO CONTINUE THE FLT TO ZZZ1 AT 10000 FT. WE ACCOMPLISHED THE CHKLIST; CHKED THAT ALL SWITCHES WERE IN THE PROPER POSITION AND LANDED UNEVENTFULLY AT ZZZ1. THE PAX MASKS DID NOT DEPLOY AND THE CABIN ALT WENT SLIGHTLY ABOVE 10000 FT. THIS WAS A VERY PUZZLING SITUATION BECAUSE ALL SWITCHES WERE IN THE PROPER POSITION WITH NO INDICATION OF A MALFUNCTION. BOTH PLTS ACCOMPLISHED ALL CREW ACTIONS CORRECTLY EXCEPT WE DIDN'T DON THE OXYGEN MASKS IMMEDIATELY AS REQUIRED BY THE QRH. THIS SHOULD HAVE BEEN OUR FIRST PRIORITY.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THAT AS THE ACFT WAS CLBING THROUGH FL280 FOR FL330; THEY HEARD A 'FAINT' HORN BUT DID NOT IMMEDIATELY IDENTIFY THE SOUND AS THE CABIN PRESSURIZATION WARNING. ONCE THE HORN WAS IDENTIFIED; BOTH PLTS AND THE JUMPSEATER; AFTER EXAMINING THE CONTROLS AND SWITCHES; DECIDED NOT TO CHANGE THE PRESSURIZATION CONFIGURATION AND BEGAN THE DSCNT. THEY REASONED THAT BECAUSE THE PRESSURIZATION PANEL CONFIGURATION WAS CORRECT; THE CAUSE OF THE PRESSURIZATION LOSS WAS SOMEWHERE ELSE. ADDITIONALLY; THEY WERE DISTRACTED BY THE COMMUNICATIONS WITH ATC AND THE DELAY IN GETTING LOWER ALTS. FOR THESE REASONS NONE OF THE FLT STATION OCCUPANTS DONNED AN OXYGEN MASK. THIS DECISION WAS NOT A CONSCIOUS OMISSION IT WAS MERELY A BREAKDOWN IN CHKLIST DISCIPLINE. THE CREW DETERMINED FROM ACR MAINT THAT THE OUTFLOW VALVE HEATER GASKET AND A BELLY DRAIN MAST FAILED.