My Joomla editors are not working properly. When I save any HTML in editor, it changes its inline CSS or show it without CSS. I should also mention that CSS is not blocked in the joomla backend in any editor.
I had the same issue. I tried various settings (mentioned below) but ended up using Sourcerer http://www.nonumber.nl/extensions/sourcerer
You can quickly configure Joomla from stripping away your HTML tags by configuring your user groups ‘Filter Type’ to: ‘No Filtering’ or to your own preference for the respective Filter Groups.
By default JCK will strip a lot of CSS and it my case it was Glyphicons.
You can also set Global Config - Editor to 'none' which should allow you to type in pure code.
Personally I use JCE Editor which I find to be more capable.