Good to know the splitter version works, and thanks for saying which shape you ended up with.
I want to check the loop detection idea before I agree with it, because I do not think there is any. As far as I know nothing in the game refuses a loop or zeroes one. So if a direct loop went dead there is probably another reason, and I would rather find it than guess at it.
One thing worth trying while I look. An outreach centre needs workforce and energy together. If it runs short of energy it banks workforce until it cannot hold any more, then deliberately holds its own input cable so the workforce goes somewhere useful instead. From outside that looks exactly like the line dying for no reason. If your block is tight on power, that could be it rather than the wiring. Worth watching whether the ones that go quiet are the ones furthest from your generators.
That is a guess until I have sat down with your shape though, so treat it as something to try rather than an answer.
Either way, if a machine can hold its own cable and say nothing about it, that is on me and not on your wiring. It should tell you.