When the user hits the Refresh button, or presses F5, the page will be reloaded, but the BHO won't receive the DocumentComplete event again, only the DownloadComplete. This means that refreshing a page with PeteSearch on won't run the DOM manipulation callback code I hang on the document event, and so the plain search result page will be shown.
I haven't got much information on this one, since this is a low-priority bug for my purposes.