Medium Transport; Low Wing; 2 Turbojet Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 14
Distraction; Communication Breakdown; Situational Awareness
Conflict Airborne Conflict; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance
Human Factors; Procedure; Aircraft
Aircraft X entered my airspace westbound at FL400.  The pilot asked for FL430 at some point in my airspace and I told him there was a recent report north of his position of continuous light chop.  Aircraft X asked for the winds at FL430 and I asked the other aircraft and he gave the winds.  After a couple minutes; Aircraft X requested a climb to FL430 and there was no traffic; so I gave a clearance to climb.  Aircraft X was level for several minutes and I had Aircraft Y enter my airspace at FL410 eastbound.  Aircraft X and Aircraft Y were on opposite courses and head on; separated by altitude.  When they were about 10 miles apart; Aircraft X advised that the temperature was too warm and needed a descent; he also advised that he saw the traffic at FL410.  I told the pilot I would get him lower as soon as they passed and I had separation.  Shortly after that; Aircraft X advised he needed a turn and lower.  I issued a 30 degree right turn and told the pilot I would have lower shortly.  Aircraft X advised that they could not keep altitude and had started down and needed lower.  At this point; the aircraft had passed but I did not have standard separation.  I saw in the data block Aircraft X showed FL427 and they looked about 3 miles apart and I advised lower would be available shortly.  The next radar hit showed the altitude at FL424 and descending.  I soon had separation and descended Aircraft X to FL400 and they continued the flight.  I advised the CIC that separation was lost on the 2 aircraft due to warm air at FL430.
While established at FL400 and one hour into our flight we calculated that had burned sufficient fuel and our weight and temperature would permit a climb to FL430.   We asked for FL430 and was cleared to FL430 with no restrictions.  The aircraft climbed normally at 500fpm initially and I decreased rate to 300fpm above 42;000 feet.   At level off we indicated 195 KIAS which would be expected.  The flight manual showed that we should accelerate to 205 KIAS given our weight and OAT.  Shortly after level off our airspeed was stable but then started to decrease.  I also noticed traffic ahead 2;000 feet below us.  I advised ABQ Center that we would need lower and he advised of the traffic.  A short time later as our airspeed continued to slowly decrease I advised ATC that we would not be able to maintain altitude. At this time we had slowed to Vref+10 at 180 KIAS.  ATC issued a right turn of 30 degrees.  I could visually see the traffic passing off our left side below as I began my right turn which slowed the aircraft even more. At this point the aircraft had slowed to Vref at 170 KIAS.  I disengaged the autopilot to prevent a high altitude stall and held Vref on my AOA.  By doing so the aircraft began to descend and I advised ATC that we were in a descent.  Immediately following this transmission and prior to declaring an emergency decent we were given a clearance to FL400 and cleared on course.  After no other discussion with ATC about the decent we had assumed there was no loss of separation with the traffic.  After a couple hand offs down the road we were advised of a possible loss of separation and to contact ABQ center on the ground which we did. While I have not flown this particular aircraft at FL430; I have been there many times in other CE-650's.  I have recalculated the performance numbers again and show that given the OAT; aircraft weight and power setting we should have been able to accelerate.  The aircraft performed normally when reaching FL400 for another 500 miles and eventually were able to climb to FL430 with no issues.  These events occurred very rapidly but I feel this description is accurate to my best recollection.
ZAB Controller describes climbing an aircraft to its requested altitude; then after 10 minutes the pilot advises the CPC that they need to descend.  CPC tells pilot in a few minutes for opposite direction traffic; pilot descends anyway causing a loss of separation.