The reason why it does not prompt it is because the browser needs the page to phyiscally to refresh back to the server. A little trick you can do is to perform two actions with the form. First action is onsubmit have it call your Ajax code. Also have the form target a hidden iframe.
<iframe src="ablankpage.htm" id="temp" name="temp" style="display:none"></iframe>
<form target="temp" onsubmit="yourAjaxCall();">
See if that causes the prompt to appear.