It’s likely not anything you are doing wrong but, rather, a misbehaving plugin. There is a lot of ugly code out there that causes widget zones to freak out on the admin side.
Try killing all of your plugins first, do you still have the problem? If not, turn them back on a few at a time until you find the culprit.
If you have access to your PHP log, clear the log and refresh the page. Pull your log, get rid of all the PHP Strict Standards warnings that are everywhere since 3.6, and what’s left probably contains your error.