jQuery:
<script>
$(document).on('click.bs.dropdown.data-api', '.dropdown.keep-inside-clicks-open', function (e) {
e.stopPropagation();
});
</script>
HTML:
<div class="dropdown keep-inside-clicks-open">
<button class="btn btn-primary dropdown-toggle" type="button" data-toggle="dropdown">
Dropdown Example
<span class="caret"></span>
</button>
<ul class="dropdown-menu">
<li><a href="#">HTML</a></li>
<li><a href="#">CSS</a></li>
<li><a href="#">JavaScript</a></li>
</ul>
</div>
Demo:
Generic: https://jsfiddle.net/kerryjohnson/omefq68b/1/
Your demo with this solution: http://jsfiddle.net/kerryjohnson/80oLdtbf/101/