Oftentimes your editor will screw up the "Read More" buttons. For example, the TinyMCE editor (the default for most Joomla installations) will "fix" what it thinks is bad HTML code, which breaks many types of Read More buttons.
If you're using TinyMCE, you can turn off its "clean up code" option. If you're using another editor, it may have a similar feature that you can turn on/off. The JoomlaFCK editor also tampers with HTML.
In extreme cases, you may have to tell Joomla you're using "no editor" and manually fix up the HTML in your editing window.