LOSS OF CABIN PRESSURE. EMER DECLARED AND DIVERSION TO ALT ARPT MADE.

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WE WERE FLT XYZ FROM MIA TO TLH. CLBING THROUGH FL270 FOR FL310; WE ENCOUNTERED VISIBLE WING ICING AND TURNED ON THE WING AND TAIL ANTI-ICE. WE WERE ALREADY RUNNING THE ENG ANTI-ICE. AFTER ABOUT A MIN WE GOT A L DUCT OVERHEAT LIGHT AND AUTO-SHUTDOWN OF THE L BLEED. AS COULD BE EXPECTED; THE CABIN PRESSURE BEGAN TO FLUCTUATE; BUT THEN IT BEGAN CLBING RAPIDLY (CABIN VSI PEGGED). THE FO REQUESTED LOWER FROM ATC; AND INFORMED THEM WE WERE HAVING A PRESSURIZATION PROB; AS I TRIED TO CTL THE CABIN PRESSURE. WE WERE CLRED TO FL200 AND I BEGAN A DSCNT WHILE KEEPING THE PWR UP ON THE R SIDE TO KEEP BLEED PRESSURE UP. WE TURNED OFF THE WING AND TAIL ANTI-ICE BUT THE CABIN CONTINUED CLBING. WE RAN THE 'DUCT OVERHEAT CHKLIST' BUT IT WOULD NOT RESET. WITH THE CABIN RAPIDLY APCHING 10000 FT; WE ASKED FOR LOWER BUT ATC SAID THEY COULD NOT COMPLY. NOT WANTING TO RISK PAX INJURY; AND THE PRESSURE SHOWING NO SIGN OF STABILIZING; I DONNED MY OXYGEN MASK AND WE DECLARED AN EMER AND WERE IMMEDIATELY CLRED TO 10000 FT. AS WE STARTED DOWN; I MADE 1 MORE ATTEMPT TO RESET THE L VALVE AND IT WAS SUCCESSFUL. WE LEVELED AT 10000 FT WITH THE CABIN ALT AT 10000 FT (THE PAX MASKS DID NOT DEPLOY AND THE CABIN PRESSURE LIGHT DID NOT ILLUMINATE). WE WERE ABOUT 30 MI FROM TPA SO I ELECTED TO LAND THERE. WE INFORMED TPA THAT WE NO LONGER HAD AN EMER CONDITION; AND WE LANDED NORMALLY WITH NO SPECIAL ASSISTANCE OR EQUIP REQUIRED. THERE WERE NO PAX INJURIES AND WE CONTINUED ON IN ANOTHER ACFT. THIS IS THE SECOND SUCH PRESSURE LOSS I HAVE ENCOUNTERED IN LESS THAN 1 YR (THE FIRST WAS A PRESSURE CTLR PROB; WHILE THIS WAS TRACED TO A FAULTY BLEED CROSSOVER VALVE). WHILE IN BOTH CASES THE CREW WORKED WELL TOGETHER; I BELIEVE SOME NEW PROCS SHOULD BE ESTABLISHED FOR A GRADUAL LOSS OF PRESSURE SUCH AS WE ENCOUNTERED. THERE IS NO PROC OUTLINED TO TURN OFF ANTI-ICE; ETC; ALTHOUGH THIS IS AN OBVIOUS THING TO DO; AS WELL AS KEEPING PWR UP WHILE DSNDING TO HELP BLEED AIR SUPPLY. ALSO; THE BLEED AIR SYS ON THE MLG SEEMS TO BE OVERLOADED AT TIMES WHEN FULL ANTI-ICE IS USED AT MAX CABIN DIFFERENTIAL. THIS COULD BE A PROB IF 1 BLEED IS LOST AT HIGHER ALTS. I WOULD ALSO LIKE TO SEE THE FAA ISSUE SOME GUIDANCE AS TO WHEN THEY CONSIDER A SLOWLY RISING; BUT UNCTLABLE CABIN AN EMER SIT.