OK - progress. ALL cables are tight and intact and the connectors are good, including around the battery. I've managed to reproduce the behaviour by twiddling on the rollers for 15-20 minutes with frequent gear changes until the whole thing goes dead. Plug in the Junction A box, slip the USB end in and out of a socket quick-sharp (less than a second, so absolutely no meaningful recharge) and the system is up and running again.
With this info, I've now got in touch with Canyon UK Service as a warranty issue.
The important thing here is reproducibility. I appreciate that I could have just handed the problem straight over to Canyon, but there's benefit to getting a handle on the issue myself first. The most obvious is that it could just have been a loose cable. But there are also some advantages when it comes to warranty. The better I can describe the problem, the easier it is for Canyon to either (a) start to sort it or (b) justify it to themselves that new bits are required and get them out pronto. I believe they'll also be more inclined to help because I've made an effort and I'll also be less likely to be fobbed off with a "turn it off and on again" type response. The goal here is to get it sorted as quickly as possible.
@jay clock - thanks for the heads-up. You know the LBSs of which I speak.