It's because of this code - just remove it

 $("#intro-slider").hover(function() {
  $("ul#slides").fadeIn(5000);
 }, function() {
  $("ul#slides").fadeOut(5000);
 });

The jquery cycle plugin does the fading of the slides, so I'm not really sure what that bit of code was intended to do.

I still see it on the page... that code causes the entire slider to fade out, but only when you hover over it.