From the support portal, you have control to reply to aticket, close a ticket or add another party on to the ticket thread.  Just use the control buttons highlighted inthe picture below.

When you are satisfied that your issue is resolved, you willbe invited to close the ticket.   

All resolved items will be automatically closed after 48hours.

Here is a screen shot of the window used to add another recipient on to the ticket thread.

 When the ticket status says "Resolved" you will be invited to close the ticket yourself from the portal as your confirmation that the issue is in fact resolved.