On hover, open up a hidden div and delay it’s closing.

$('#footerlinks ul li').hover(
function(){
  $(this).next('li.footer-hidden').animate({ "max-width": "1000" }, 'fast');
// This only fires if the row is not undergoing an animation when you mouseover it
},
function() {
  $(this).next('li.footer-hidden').delay(3000).animate({ "max-width": "0" }, 'fast');
});