Do browsers support autocomplete for ajax loaded login forms at all?

My problem is, that the browsers' (IE&FF) autocomplete does not work for my login form.

I have a webapp with CakePHP & jQuery. To allow visitors to login/register unobtrusively. The login form is inside a div, which is loaded via AJAX. (This enables logging in without a page reload.)

The browsers do recognize it as a login field, as they prompt me to save the credentials when clicking login. And they really do save the username/password, as they appear between the saved ones in the browser settings. But the saved username/password is never entered automatically. They do not appear pre-entered when the page loads. When I start typing in the username, the username appears as a suggestion, but even when you select it, the password is not entered next to it. Why? How can I get this working?

That you can test it yourself, here is a simple AJAX login form:

http://gablog.eu/test/ajaxlogin.html

It loads the following login form, if you go to the url below, autocomplete will work for just the plain form, so it is not a problem with the form itself, but rather that it is AJAX loaded: http://gablog.eu/test/loginform.html

The layout:

<div id="user-bar">
    <script type="text/javascript">
        $(function() {
           $("#user-bar").load('loginform.html').html();
        });
    </script>
</div>

The view loaded (when not logged in):

<form id="form-login" action="" onsubmit="login(); return false;">
    <input type="text" id="username" name="username"/>
    <input type="password" id="password" name="password"/>
    <input type="submit" value="Login"/>
    <div id="login-error" class="error-message"></div>
</form>

<script type="text/javascript">