I found the answer [here][1]:

 - If the install uses FTP for updates (and prompts for credentials),
   automatic updates are disabled. (I found [this answer][2] which will tell you how to avoid using FTP.)
 - If the install is running as a SVN or
   GIT checkout, automatic updates are disabled
 - If the constants
   DISALLOW_FILE_MODS or AUTOMATIC_UPDATER_DISABLED are defined,
   automatic updates are disabled
 - If the constant WP_AUTO_UPDATE_CORE is
   defined as false, automatic updates are disabled
 - Your WordPress
   install also needs to be able to contact WordPress.org over HTTPS
   connections, so your PHP install also needs OpenSSL installed and
   working
 - Wp-Cron needs to be operational, if for some reason cron
   fails to work for your install, Automatic Updates will also be
   unavailable

[This plugin][3] will test these things for you.


  [1]: http://make.wordpress.org/core/2013/09/24/automatic-core-updates/
  [2]: https://wordpress.stackexchange.com/a/23175/4661
  [3]: http://wordpress.org/plugins/background-update-tester/