Check out http://mainlypiano.com/ and start typing in the search box ("dav" will get you several results).
Notice that the search box goes below the middle light purple box. There's no z-index here to cause an issue. If one removes the relative position of the light purple box, the search results menu shows in its entirety. That's weird, isn't it? (That messes up the "favorite albums" text there, which is the point of the relative position, but lets you see the error.)
Any idea why this is happening?