You are receiving incoming support emails that relate to open cases, but these emails are not creating new Case Comments.
If you observe this behavior, please see the following:
1. Check to see if Case Feed Layout has been selected on the first page of the Email to Case Premium setup wizard. With Case Feed Layout selected, Email to Case Premium will never insert Case Comments in Salesforce. Some more information on this can be found here in our documentation.
2. Your email server should be forwarding your customer emails to Email to Case Premium rather than Salesforce Email-to-Case (Standard).
Check to make sure your email server is not forwarding customer emails to any of the Email2Case routing addresses listed under Setup > Customize > Cases > Email-to-Case.
Rather, your email server should be forwarding customer emails to the routing address you created during the Email to Case Premium initial setup. Note that your organization's address will be unique.