I figured out the problem and fixed this issue.
Issue was i have used div instead of ul for the drop down. It's closing when you click other than ul.
I just replaced this
<div class="dropdown-menu span3" style="background:#0C0;">
With ul > li
<ul class="dropdown-menu span3" style="background:#0C0;">
<li>
<form....
</li>
</ul>