Update: I’ve just found that the problem doesn’t occur when I use the search widget. The navigation search still needs a double-click. Could you please take a look at the CSS settings of the nav search and the result box? Maybe there’s a conflict between the two properties.
That’s strange, it almost looks like a bug with the focus. Any chance you can report it to the plugin author? They might know why this could happen/what we can do to fix it. Maybe just removing focus once the results are shown would fix it.
Nevermind, Tom. I’m now using Dave’s WordPress Live Search and it’s almost perfect. I have one issue with CSS but I’m opening a new ticket to solve it.