Ok this doesn't really make sense. I pasted in your HTML and it worked fine. Why will it not work with the HTML the editor generates on its own then? Here is an example of what it generated and did not save the image:
<div>Should be a cat under this!<br><img src="http://hcecorp.com/HCECProject/uploads/Sample_Picture04.jpg" border=0></div>
<div> </div>
<div>Should be a cat up there!</div>