ZMA CTLR EXPERIENCED OPERROR AT 20700 FT WHEN LEADING DEP ACFT SLOWED AND WAS OVERTAKEN BY A SUCCEEDING DEP ACFT.

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DURING A VERY BUSY PERIOD OF HVY TFC; I WAS WORKING RADAR SECTORS 41/42 COMBINED FOR MORE THAN 2 HRS ON POS; WHICH INCLUDED METERING FOR FLL (N RWY) AND MULTIPLE ARRS FOR BOTH MIA AND FLL AND SATELLITE ARPTS. THE MAJORITY OF THE COMPLEX TFC WAS IN SECTOR 42 AND I DID NOT ASK FOR THE SECTOR TO BE SPLIT BECAUSE IT WAS ALREADY TOO BUSY TO DECOMBINE. THE ERROR OCCURRED IN SECTOR 41. MIAMI WAS OPERATING ON A W OP; WHICH ADDS TO THE COMPLEXITY AT BOTH JUNUR/FLIPR AND DEKAL. I WAS WORKING APPROX 16 ACFT AT THE TIME OF THE INCIDENT. BOTH THE LJ35 AND THE B762 DEPARTED MIA ON THE EONNS TRANSITION AND CAME TO ME CLBING TO 16000 FT AT 6-7 MI APART AT COMPARABLE SPDS. I ISSUED CLB CLRNC TO BOTH ACFT TO FL230 AND OBSERVED DURING THEIR CLBS THAT THEY MAINTAINED THEIR SEPARATION AND WERE BOTH INDICATING AT 370-380 KTS GS. I WAS SATISFIED THEY WOULD REMAIN SEPARATED; AND THEN FOCUSED MY ATTN ON THE TFC IN SECTOR 42. AT THE TIME CONFLICT ALERT ACTIVATED; THE LJ35'S GS DROPPED TO 330 KTS; AND SEPARATION WAS LOST AT AROUND FL207. I IMMEDIATELY ISSUED A VECTOR TO THE B762 (HE WAS THE FOLLOWING ACFT) TO A HDG OF 090 DEGS AND STOPPED HIM AT FL220. DURING THE REPLAY ON THE FALCON SYS AT THE ZMA WATCH DESK; I SAW THE GND SPD OF THE LJ35 DECREASE BY ALMOST 50 KTS; AND CONFLICT ALERT DID NOT ACTIVATE UNTIL SEPARATION WAS ALREADY LOST. I FEEL THAT THE SECTOR WAS TOO BUSY TO REMAIN COMBINED; ALTHOUGH I DID NOT ASK FOR SECTOR 42 TO BE SPLIT BECAUSE IT WAS ALREADY TOO BUSY; I DID NOT ANTICIPATE THE RAPID DETERIORATION OF SEPARATION ON THE SUBJECT ACFT. AT NO TIME DURING MY MORE THAN 2 HRS ON POS DURING THIS HVY TFC DID THE SUPVR COME OVER TO ASSESS THE SITUATION; NOR EVALUATE THE TSD FOR POSSIBLE SECTOR DECOMBINATION. AT CTR IT IS TYPICAL FOR US TO BE VERY BUSY DURING THE HOLIDAY TFC PERIODS; AND AS USUAL; WE WERE SHORT STAFFED AND MOST CTLRS ROUTINELY GO OVER 2 HRS ON POS. THIS CAN CAUSE FATIGUE VERY QUICKLY; AND THAT WAS THE SITUATION IN MY CASE. HAD THE SECTORS BEEN SPLIT IN A TIMELY MANNER; I WOULD HAVE BEEN ABLE TO FOCUS MY ATTN TO ALL AREAS OF MY SECTOR; AND I WOULD HAVE MOST LIKELY NOTICED THE DEVELOPING SITUATION IN TIME TO ENSURE SEPARATION.