Can you post here HTML code of that div only from the file's source as well as source code of the div from IU's back-end editor (view source option)?
If you add CSS style directly to the DIV being edited (either via ID or CSS class) then it can not be removed using IU's content editors (both front-end and back-end). It seems to me like you have styles applied to
div > span and text is within
<span>, so when you remove everything with the editor, you remove the span too (or whatever inline element you have, span is most common), so the style(s) get deleted.