C650-VII CREW AT FL450 COULD NOT MAINTAIN ALT AND WERE ADVISED BY ZAB A DSCNT CLRNC COULD NOT BE GIVEN BECAUSE OF TFC.

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THE INCIDENT OCCURRED WHILE FLYING A DEADHEAD LEG BTWN PSP AND LBE EBOUND ON J96 BTWN CIM AND GCK. EARLIER IN THE FLT; A REQUEST WAS GRANTED TO CLB TO FL430 (OPPOSITE DIRECTION) IN ORDER TO MAXIMIZE RANGE AND AVOID CONVECTIVE ACTIVITY ANTICIPATED ALONG OUR RTE IN KANSAS. SUBSEQUENTLY ATC REQUESTED US TO DSND FOR OPPOSITE DIRECTION TFC CONVERGING AT FL430. UNDER THE PRESENT CONDITIONS OF ACFT WT AND OUTSIDE AIR TEMP; FL450 WAS WITHIN THE CLB CAPABILITY OF THE ACFT AND WAS PREFERABLE TO FL410 FOR THE PREVIOUSLY MENTIONED REASONS. THEREFORE; I REQUESTED FL450 AND WAS CLRED TO CLB. THE ACFT CLBED NORMALLY. HOWEVER; ONCE AT FL450 IT BECAME APPARENT THAT THE AIR TEMP HAD INCREASED TO THE EXTENT THAT THE ACFT WOULD NOT ACCELERATE AND SAFETY OF FLT DICTATED THAT A DSCNT WAS NECESSARY IN ORDER TO MAINTAIN A SAFE FLYING SPD. A REQUEST WAS MADE TO DSND TO FL410. CTR RESPONDED THAT OPPOSITE DIRECTION TFC WOULD DELAY OUR DSCNT AND WE WERE TO MAINTAIN FL450. WE REPEATEDLY INFORMED ATC THAT AN IMMEDIATE DSCNT WAS NECESSARY. THE CTLR THEN VECTORED THE OTHER ACFT; BUT STILL WOULD NOT PERMIT US TO DSND. WE AGAIN INFORMED THE CTLR THAT A DSCNT WAS NECESSARY AND THAT WE WOULD BE WILLING TO ACCEPT A TURN IN ORDER TO EXPEDITE OUR DSCNT CLRNC. ATC THEN VECTORED OUR ACFT BUT STILL DID NOT GRANT A DSCNT. DURING THE ENTIRE EVENT; WE MONITORED THE OTHER ACFT ON OUR TCASII. FACED WITH COMPROMISING SAFETY OR DEVIATING FROM AN ATC CLRNC; A DECISION WAS MADE TO START A DESCENT IN ORDER TO ACCELERATE. WE INFORMED ATC THAT WE WERE DSNDING AND FINALLY ANOTHER CTLR (SUPVR) BROKE IN AND ACKNOWLEDGED OUR DSCNT 'DUE TO TEMP;' BUT STILL DID NOT CLR US TO DSND. WE HAD DSNDED TO APPROX FL444 WHEN ATC FINALLY CLRED US TO FL410. WE WERE INSTRUCTED TO CALL ZAB ON THE GND UPON LNDG ABOUT A POSSIBLE PLTDEV. WE WERE INFORMED DURING THIS CALL THAT SEPARATION REQUIREMENTS WERE COMPROMISED. APPARENTLY THE REQUIRED 5 MI SEPARATION WAS REDUCED TO '4 POINT SOMETHING.' DURING THE ENTIRE EVENT; THE CONVERGING ACFT WAS MONITORED ON OUR TCASII. NO TA OR RA WAS RECEIVED FROM THE TCASII. DEV FROM AN ATC CLRNC WAS NECESSARY IN THE INTEREST OF SAFETY AND ATC WAS IMMEDIATELY NOTIFIED OF THE DEV. ALTHOUGH I AM NOT BLAMING ATC FOR THE OCCURRENCE; I DO NOT FEEL THAT ATC DID ALL THAT WAS POSSIBLE IN AN EXPEDITIOUS MANNER IN ORDER TO ALLEVIATE THE SIT.