No splitters at all, actually. The coaxial cable comes straight in and to the modem. I might have a quick look outside, but I don't think that's the problem. It's the regularity of the connection loss that's puzzling.
And with 24/7 support I'm not sure if it would be kinder to call at 1am or at 6am, both seem pretty unpleasant times to be troubleshooting