That was my first thought Val - If the fires go out for whatever reason, then they aren't going to respond to auto-throttle or manual commands...
but then again, I'm sure the AAIB would have mentioned the obvious loss of EGT on the trace if it was a flame-out, rather than this 'failure to respond to commands" - so it would appear they went into snooze mode at idle?
Yikes indeed, and mucho kudos to the crew.