When using vw sizes on webkit browsers, a well-known bug can occur where they do not update when the window is resized. The typical workaround for this issue has been to employ javascript to force a redraw of the element by reassigning the z-index upon resize. For example:
CSS:
#siteSearch input { font-size:10vw;}
Javascript/jQuery:
function resizing() { $("#siteSearch *").css("z-index", 1) }
window.onresize=resizing;
However, this solution does not seem to work with :before content. I have created a demonstration on JSFiddle to showcase this issue. When you resize the window, the search box/text adjusts its size correctly, but the magnifying glass icon (which is an icon font character generated by :before content) does not. To see updates for the icon, you need to refresh the page or rerun the JSFiddle. In Firefox, the icon may also display improperly due to cross-site issues, though that is unrelated - sizing works fine there.