Issue: When you are logged in the search bar shows in the correct place, but when you are logged out the search bar shows as too far down the page.
Resolution: The position of the search window is based on an offset from the top of the screen. When you are logged in to wordpress there is an admin bar which pushes the content further down the page.
When setting your Search Window Position make sure to check your site when you are not logged in to make sure that the search bar displays correctly.