The Quick Edit Tab will only work if you are actually logged into your Online Store Manager. Therefore, make sure the URL you are viewing your store in is thesame as the URL you are logged into for the admin. In other words, if you are logged into your admin by way of https://[domain].s4shops.com, please make sure you are viewing the site with the http://[domain].s4shops.com URL as well. (otherwise, your session cookie may not recognize you as logged in to the admin)
Also, please be sure to check your Administrative login permissions to ensure your login has access to the Admin Design bar. To verify this, go to Settings >General >Administrator Access. Click on your specific login name and check for the appropriate permissions. Under the "Design" heading, look for the last checkbox labeled "Admin Design Bar" and make sure it is checked.