BOAC, Parabellum,
I would suggest it's not likely to be satellite for BT due to their huge wire infrastructure.
BOAC - It depends where you live and how long the various pipes & cables have been there. One possible cause is that the various folks who dig up roads & pavements have hit the BT lines along the way. When cable was installed in our area, the contractors were a tad cavalier about where & how they dug - they cut off all the BT phone lines on our close which took a major job to resplice them. They also caused electrical supply problems that took a few years to manifest themselves, and while the local supply company could see the symptoms of the problem, in tracing the fault they ended up fixing three separate problems caused by the cable contractors.
If this is the case then the only route to you is to keep pestering BT every time the fault occurs until they get the message. When I last spoke to BT support they were able to run a remote test on the line while I was on - it's not specific enough to tell them the cause, but it can prove that the line is faulty (in these cases they tend to blame your equipment first
)
Keep plugging away and feel free to write letters to the management - that usually gets a response