bearfoil, "Deponent sayeth naught."
(Meaning I am a EE not a pilot. You guys are the experts on how planes can misbehave in the air.)
I will note that we've not established the minimum "allowed/possible" time between ACARS messages. For that I'd need a copy of the Inmarsat specifications for that mode. I suspect the channel is very low data rate and there may be a hold-off interval. That hold-off interval MAY vary with "history". Until we know these details I'm not sure we can find most of the gaps HN39 found. The two really long ones need explanation. The others may be artifacts, especially if a message had to be resent for whatever reason. (I can almost see a potential for such congestion if we consider all planes that might be in AOR-W's footprint and the toilet configuration errors from AF-447 suggesting some small level of traffic is normal.)
This is one area BEA needs to explain a little more, IMAO. Can they explain the precise timing or is there something to those two long gaps. (And as I wrote this I had a "duh" moment. Yes, there IS a minimum interval between messages. During that interval data is coalesced into more compact messages than if they were sent one at a time. So an extra few seconds could very well be a transmission that needed to be sent a second time.