Art-Deco,
I've remarked in the past that the Inmarsat satellites and protocols are designed to work well within a deluge. I dug into references (the ITT handbook) and looked at the charts. Rain attenuation at Inmarsat frequencies is a bit under 2dB per km in a 25mm/hour rain storm at sea level. So in the very middle of a storm at low altitude the Inmarsat communications probably can become lost, at sea level. At FL350 there is less rain and less distance through it. For rain attenuation to be a factor the plane would have had to have already descended well down into the storm.
That's another useful data point. I am guessing the point where a loss due to rain becomes feasible to consider is maybe 15,000 feet give or take some.
JD-EE