See:

• https://support.mozilla.org/kb/add-search-bar-firefox-toolbar

I had this problem too, and some people seem to think that it was taken away with a later version of the browser; but its still available. All I had to do was to right click near the top of the browser and go to customize tool bar. Then, although I did not have the search bar available to move up, I was able to bring it back by hitting the restore defaults button in the lower right corner. That regenerated the search bar option for me and I could drag it up to the customizable area.