Can't reorder gallery images using WP Edit Gallery function

I created a gallery and tried to use WP edit gallery option to reorder images (drag and drop), but that functionality no longer works. I have a new (downloaded and installed myself) WP 4.0 site and tried to reorder images using both the 2014 theme and the Divi theme by Elegant Themes. The functionality was gone in both cases.

I also have an older site that was getting the beta releases prior to 4.0 being released. Since I used that site to create training videos, I know the drag and drop reorder used to work on that site, but it no longer does. Honestly, I don’t know when the function stopped working on that site.

I have looked at other threads that mention reorder or gallery plugins, but I am using none of those. Also, since I am seeing this on sites with three very different themes, I don’t think it’s theme related.

Any other suggestions would be appreciated.