Well, wifi tosses a whole other can of worms into the mix.
It's clear that something is buggering the multicast stream, wifi adds another layer of complexity to this problem, there's additional protocols involved, I'd bet it's something with WMM that's triggering the reset on the stream.
The only viable solution I'd see here, would be to bypass the Sagemcom, and segment off part of your network.
Basically, put another router behind the Sagemcom (bridge), have it pull it's own PPPOE session, remove the PPPOE info from the internet portion of the Sagemcom. All your devices will connect to the new router, and the TV's stay connected to the Sagemcom.