How do I fix auto-renewal memberships? (Auth.net)
We had the same issue in CiviCRM 4.6.4 - our configuration inside our Authorize.Net portal was incomplete and we followed the steps outlined at

http://wiki.civicrm.org/confluence/display/CRMDOC/Authorize.net+Configuration

under Automated Recurring Billing. After putting in the correct URL for authorize.net to post to, memberships started to update.

Another thing to note is it's obnoxious to test because authorize.net processes their ARB transactions once every 24 hours at something like 2am so you won't know right away if it's working.

Pulled out the relevant text here:

"CiviCRM will need to be notified of the success of recurring contributions via a Silent Post URL.  Within Authorize.net, go to Account > Settings > Silent Post URL (within the Transaction Format Settings section).  On that page, enter the URL:

Drupal: https://yoursite.org/sites/all/modules/civicrm/extern/authorizeIPN.php

Joomla: https://yoursite.org/administrator/components/com_civicrm/civicrm/extern/authorizeIPN.php

WordPress: https://yoursite.org/wp-content/plugins/civicrm/civicrm/extern/authorizeIPN.php

If you fail to do this, one-time contributions will succeed normally, and recurring contributions will be processed successfully by Authorize.net, but the contribution status will be stuck at Pending."