What does the membership automatic renewal interface look like?
After you've made the membership type as optional, you should set an additional setting on the contribution page, i.e, 


visit Contributions -> Manage Contribution Pages
Go to the Membership tab of the required contribution page.
You will see an additional column of Auto-Renew on the Membership type field.





Select Give Option on the membership type that you want to enable this option for.
Save and Navigate to the live contribution link civicrm/contribute/transact?reset=1&amp;id=&lt;page_id&gt;. This should display an option to renew the membership.