The mystery of the missing white band has been solved! I found it stuffed up the sleeve of a pair of pyjamas, which of course is the obvious place I should have looked. Except said pyjamas were two hundred miles away from where I was looking, but let's not get bogged down in the details.
The important thing here is that I now have two white bands, which makes me twice as committed, obviously. For a while there I even wore them both at the same time. Now one is languishing as a spare, ready to be called into action the next time my wrist proves too skinny to keep a simple white band attached. Note to self: never wear expensive bracelets. Another note to self: never wear expensive jewellery because there are much better things to do with your spare money. If you ever have any.