Can't edit div after applied style on it in non-source mode

I have tried the ckeditor on the demo site http://ckeditor.com/demo
and place the following content in the source code.

<style type="text/css">
#content_banner {
   width:100px;
}</style>
<div id="content_banner">Please type content here!</div>

After changed back to the view mode, I can't edit the content by double clicking on the div. The bug is happening in IE8 but not being seen in FF3.
Does anyone have meet the same problem? Is there any workaround to it if I must need to use the style?