FLC OF A B777 DECLARED AN EMER AND DIVERTED TO LAND AFTER NOT BEING ABLE TO HOLD MINIMUM CONTROLLABLE AIRSPD DURING HOLDING AT FL410.

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AFTER DEP; WE WERE ASKED IF WE COULD ACCEPT FL410. AFTER CONSULTING OUR MANUALS WE ACCEPTED THE CLRNC. PRIOR TO REACHING ZZZ VOR; WE WERE TOLD TO HOLD. WHILE ENTERING THE HOLDING PATTERN AND MAKING SEVERAL TURNS; OUR AIRSPD BEGAN TO BLEED OFF. WE THEN COMMANDED MAX CTL THRUST BUT OUR AIRSPD STILL CONTINUED TO SLOW. WE THEN REQUESTED A LOWER ALT FROM ATC BUT WERE DENIED BECAUSE OF AIRSPACE SATURATION. WE THEN DECLARED AN EMER TO GET A LOWER ALT. AFTER RECEIVING LOW AIRSPD WARNINGS THE ACFT DIVERTED AND LANDED WITHOUT INCIDENT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THAT SINCE THE ACFT FUEL AVAILABLE WAS NOT SUFFICIENT FOR EXTENDED HOLDING EXPECTED INTO THE DEST ARPT; ONE OF THE ALTERNATES WAS SELECTED. IN ADDITION; COMPANY MAINT ADVISED THAT ONE OF THEIR 2 ENGS HAD A KNOWN PROB OF NOT PRODUCING THE THRUST EXPECTED AND THAT SHOULD BE FIXED AS SOON AS POSSIBLE. THE RPTR ALSO STATED THAT HE AND THE CAPT WERE RELUCTANT TO DECLARE AN EMER IN ORDER TO GET A LOWER ALT BECAUSE OF THE BELIEF THAT THERE WOULD BE A FEDERAL INVESTIGATION AS A RESULT. THEREFORE; THE CTLR HAD TO EXPLAIN TO THE FLC THAT HE COULD NOT GIVE THEM A LOWER ALT UNLESS AN EMER WAS DECLARED. THE ACFT OPERATED WAS A B777.