And then it fixed itself.
I was just using iSync to synchronise to my Palm Zire 71 and Motorola V3, as previously detailed elsewhere. The Palm synced as expected. For no apparent reason, the V3 sync over Bluetooth failed. The PowerBook had Bluetooth turned on, and so did the phone. They simply failed to talk. And, in typical Apple fashion, the error reporting in the iSync log failed to shed any light on the problem whatsoever.
Turning Bluetooth off and back on failed to help at both ends of the link. Unfortunately, rebooting the PowerBook did help. How very Windows.