The sequence began with a loss of thrust in the No. 4 Engine. That engine had failed twice during previous flights (while cruising at FL 410 and 430). In each of those cases, the engine was restarted after descending to a lower altitude. The maintenance response to the logbook entries that noted the problems included engine inspection, fuel filter drainage and replacement, vane controller inspection and replacement, water drainage from Mach probes, and other filter replacements. None of those acts fixed the recurrent problem of the No. 4 engine.