Sat coms, 4 hours
Here are what now seem to be almost facts.
The ACARS system for the airframe did not have a satellite subscription.
The ACARS system for the engines did have a satellite subscription.
The satellite path is used when there is no VHF path available.
The engine ACARS only sends when a significant event takes place. There was no event after the top of climb and so no further messages were sent.
The Engine ACARS satellite coms system "pings" the satellite every 30 mins.
Therefore:- Since about 8 pings were received and logged the engines ran for a further 4 hours after last message at top of climb since a shutdown would have resulted in an ACARS message. The exact time is not known of course.
By the way. I am far from satisfied that the satellite system used is Iridium. Due to the low earth orbit and rapidly changing overhead satellites I would have thought that the ping might need to be more frequent.