What was found
PILOT REPORTED WHILE IN A STEADY STATE CLIMB-OUT OF FL 310, LT ENG FLAMED OUT AT 31,400 FEET. ACFT FLYING AT .68 MACH. THERE WERE NO CLOUDS AND NO TURBULENCE. CREW DESCENDED AND TRIED RESTARTS AT FL 290, FL 250, AND FL 150 WITHOUT SUCCESS. ENG RELIGHT FINALLY ACHIEVED AT 11,000 FEET. ACFT CONTINUED TO DESTINATION WITHOUT INCIDENT. ENG GIVEN A THOROUGH INSPECTION OF INLET AND EXHAUST FOR EVIDENCE OF FOD, BUT NONE FOUND. FUEL SYS CHECKED. A FULL GRND POWER RUN PERFORMED ON ENG IAW GE MM AND ALL PARAMETERS CHECKED WITHIN LIMITS. NO MECHANICAL CAUSE COULD BE FOUND FOR FLAME-OUT. THIS SAME FLIGHT CREW SUFFERED A FLAME-OUT OF LT ENG ON ANOTHER ACFT WITHIN PREVIOUS 24 HRS. ENG RETURNED TO SERVICE. (X)