When the button is clicked it is given a class of loading which doesn’t appear to be handled.
You will have to find an icon in an iconfont (preferebly already loaded in your site i think its loading glyphicons) to use and add some css like below (Not tested, modify to suit)
Let me know if that helps.
button.add_to_cart_button.loading:after{
position:absolute;
top:0;
left:0;
width:100%;
height:100%;
font-family:"Glyphicons Halflings";
content: "\e031";
background: rgba( 255, 255, 255, 0.7 );
text-align:center;
line-height:34px;
}