Generally marking a clock segment as a failure should happen when narratively appropriate - when a lead goes dry, when a resource is permanently out of reach, or just generally when it's unlikely that this avenue of investigation fails. Marking a segment is kind of like the full stop at the end of a little mini arc.
I can see how that's not clear, and we should have made it explicit, but almost any move rolled at 6 or below could potentially trigger a X for a clock. Hope this helps