Might be worth setting up a Thinkbroadband ping monitor as swoop suggested, if you don't already have one running. Would show the dropouts every 34 mins whilst in modem mode, on the graph that it produces.
As an aside, I've got one of the SH3's coming on Friday. Pretty sure I'm still on an old Motorola BSR 64k (If anyone knows about the Telford headend could confirm?), so hopefully not letting myself in for a world of pain
