I'm not sure that a screen shot will help, but I will,

go to your demo and try this. 

handle issue

1. Add a div after the table in your demo and click on it.. handles appear

2 click inside the existing demo table and add a div.  Handles will not show.

 

Now create a new div and try to style it with any color border solid and click anywhere in the editor window,

the style doesn't hold and if you update it or add the code manually cuteEditor removes it.

dm