I can reproduce it with Safari if I enlarge the font size (Cmd +), and it looks like this will happen with 
*any* browser.

Main cause is that the with of the sidebar is set in pixels, while the size of the Quick search box (and the 
sidebar text as well) scales with the font size.

One possible solution would be to set a fixed pixel width for the Quick search box via css. (This wouldn't 
prevent the sidebar text from overflowing, though, but that usually happens only with *very* large font 
sizes, as the browsers first try to wrap the text to fit it into the box. Only if individual words won't fit, 
they overflow.)

Another possible solution would be specify the sidebar with in ems.