Are you talking about the search bar in the top right in Firefox? If so, I think you may be trying to delete google suggestions, which automatically suggest common search terms which match the letters you are typing in, as you are typing them. I just tested it and they don't get deleted when you delete them individually, as other autocomplete entries do, they seem to be persistent.
If you don't want the suggestions at all, just right click anywhere on the search box and untick 'Show Suggestions' - if you are using a different browser or are talking about a different problem, please explain further.