It turns out the problem was the theme. (I think).
The homepage has a layout like this:
One large area for the most recent post at the top, then two columns below it, each with smaller areas for posts. The most recent is **always** displayed at the top, but then below that, the sticky posts are displayed, followed by all the most recent posts (except the very most recent which is at the very top).
Had me scratching my head. I guess it will do.
