Check that the Editor Profile Parameters allow IFrames

In the JCE Control Panel, click on the Editor Profiles button.

Click on the Profile name that the user, usergroup or component is assigned to, eg: 'Default'

Click on the Plugin Parameters tab, then on the Media Support tab.

Check that the Allow IFrames is set to Yes.

Configure Joomla! Article filters

By default Joomla!  'cleans' content on saving, removing script tags, event attributes (such as onclick, onmouseover etc.) and style tags.

A simple article parameter change is all that is required to fix this.

Joomla! 1.5

See this article - 

Joomla! 2.5 and Joomla! 3

  1. In the Joomla! Global Configuration, click on the Text Filters tab.
  2. For the Super Users group, or any other trusted user group, set Filter Type to No Filtering. Make sure that you only set this option for user groups that can be trusted as setting the Filter Type to No Filtering will essentially allow the user to include any html in an article. 

RSFirewall scambles tags

If you have RSFirewall installed, please read this article -