did you try Ajax settings from the admin menu?
Sorry for the delay. Yes I have the Enable AJAX box checked and the Disable AJAX Course Editing box unchecked.
It's definitely not the site-wide AJAX settings. In a single course, I can enable to drag and drop by changing the course format from Weekly Format - CSS to Weekly Format. So it must be something about the Weekly Format - CSS. Is there a flag I need to change on that format, or is that format just not setup to use drag and drop?
In case you haven't found this already - the Weekly CSS format doesn't yet support ajax. See MDL-9306.