The current search interface utilises a search box which replaces the location bar and introduces a number of new interface elements. This interface has a number of disadvantages and usability issues. Here are just a few examples:

 * The replacement of the location bar confuses the relationship between the search and the location on which that search is being located (see https://bugzilla.gnome.org/show_bug.cgi?id=325086). 
 * That search functionality is accessed through a button de-emphasises that functionality and also means that it takes more effort to access it (see https://bugzilla.gnome.org/show_bug.cgi?id=602008).
 * It is difficult for users to understand how to close the search interface (see https://bugzilla.gnome.org/show_bug.cgi?id=595660).

Each of these issues would be solved by using a dedicated search box. Garrett le Sage has demonstrated what this could look like in his mockups: http://linuxart.com/log/archives/2009/07/24/nautilus-streamlined/.

The main advantage of a permanent search box is its simplicity. It would make Nautilus's search interface clearer and easier to understand as well as easier and more obvious to access.