I think that I can see what you are talking about. When I view the content it looks the same as it does on the page, then when I edit it the styling seems to disappear. When I check on the source I notice something that seems incorrect. In the style that is applied to the text it looks like this:
So it seems that some extra quotes are being added to the source that are preventing it from displaying correctly. To check what may be causing this take a look at the default value for your iRite editor. If there is any entity encoding it could be causing this to happen. Take a look there and see if you can adjust it to stop this from happening, if there is encoding going on you can test it by removing it then see what the result is when you use the iRite editor to update the text.