sd666, there is another reason I've not touched upon because it is so obvious for the ACARS transmissions to be blocked during some intervals.
Other aircraft are in the air. And they have position report messages to file. Several such could have taken place in the time window specified. I do not know the full ACARS protocol for transmission slots, transmission handshake, and who controls when aircraft send data packets are all unknown. However, two aircraft trying to send a message at the same time would interfere with each other.
Since ACARS is not an emergency sort of channel it is possible the protocol requires some form of wait between transmisson periods. During that wait other planes could request a slot. Then the satellite would designate the next plane to send a data packet. (The strategy after a packet's receipt acknowledgment would call for a small random delay with a very short time slot allocation request message being sent at the end of the delay. Planes heard would be serviced one at a time by the satellite granting them a transmission time slot.)
Regarding a spin maybe driving the satellite out of the antenna beam the satellite is geosynchronous. The antenna has a 40-45 degree cone to its 3dB or half power point judging from its claimed gain. The satellite use was probably the one just about over the coast of Africa. The plane was virtually under it in the N/S plane and well inside the satellites footprint E/W. If the plane spun fast antenna tracking would not work and it would probably go (barely) outside the beam. If the spin was a "leisurely" 2 minutes, as the gaps suggest, the beam COULD be automatically steered to maintain its aim at the satellite. (I was involved with a completely different use for Inmarsat satellites. And our antenna easily tracked something as leisurely as 2 minutes. I heard that some Arabs mounted antennas on top of their cars in Saudi Arabia and drove around using Inmarsat as their "cell phone" before there were cellphones. Cars turn. But the antenna tracked it.)
That's the basis for my doubting the transmission gaps are caused by the antenna aim being off the satellites.
On the other hand, the antenna is a patch antenna. So it's steering ability is somewhat limited to a cone about 75 degrees from vertical. A heavy bank could position the antenna so that communications was very marginal. A really severe bank could literally hide the satellite from the antenna.
One last observation I believe I noticed in the BEA report (English version) was that there were no indications of attempted ACARS transmissions that did not make it through. What I don't know is whether my mind is playing tricks on me or not. Bad aim would lead to partial messages with high error rates. That would cause them to be tossed. But the system would likely record the event as a lost message.
(Time for me to shut up. I'm getting into stuff to obscure to try to detail for probably no great purpose.)