Cannot re-order the blocks of Drupal 7 site
If there's no javascript error in the console, and you have a lot of blocks, and are using the Suhosin extension, you may be hitting a Suhosin limit. If that's the case, you will need to increase the relevant values there. There may be more information in your server error log.

More info: http://www.hardened-php.net/suhosin/configuration.html#suhosin.post.max_vars