It's a Thorn Tandem. We've done about 1-2000 miles a year.
The wheel was rebuilt by SJS with CSS Rigida rims a couple of years ago, it was fine until last March when spokes started breaking (it looked like mid-spoke corrosion), so I replaced them all as described. I have no idea whether this is related to the screws coming undone, but I mention it so that someone more knowledgeable has all the information.
My current plan is to order a new set of screws from Rohloff, if I can work out the part number, and then do an oil change, which was due next month anyway.
But I'd still like to know why this happened in case it happens again. The Rohloff has been pretty good and maintenance-free (apart from oil changes) til now. I'd like to be able to continue to be confident in it.