This bug was mentioned recently, but I think I've got a 100% repeatable test case that you can try it on.
For me at least, if you use the numpad to invoke an item, the number you selected will show up as the initial search field the next time you bring FARR up, but only if the item is a URL. It seems to happen both with .URL files and with URLs in aliases. I don't seem to ever see it happen with anything else.
Hopefully this will give you a better idea where the problem might lie.