Not exactly sure what happened, but now the Submit Credit Card Membership option is not available in the Admin side of a Joomla install (v3.5.1). All seemed to be working fine, but then it disappeared. I tried recreating the Payment Processor and selecting it in the Contribution Page, but no luck. Then I opted to update to CiviCRM to 4.7.8 to see if that was the issues, still no luck. I am hoping it is just some sort of reset, otherwise our site is dead in the water with a conference coming up.
Looking at your issue: See CRM-15394
David Greenberg added a comment - 30/Sep/14 12:03 PM The back-office 'Submit Credit Contribution' feature is only available when the site has at least one configured payment processor of the type that allows credit card data to be entered within CiviCRM forms. This includes Paypal Pro, Auth.net and iATS. The link is hidden on the demo because the configured 'Test Processor' does not support this.
I am seeing the same thing in the Joomla Demo - I think you have found a bug. Please report it at https://issues.civicrm.org
Note this is only in Joomla, Drupal demo shows the link.
Update: Adding an authorize.net account on demo made the link appear. You could test your payment processor account on another instance to see if that's the problem.