There's a section labeled "Contact Us" at the bottom of every page of the QVC website. If you're having trouble accessing live chat, you may want to try a different browser or clear your cache and cookies. Even if the connection problem is on QVC's side, these simple steps will help you get to where you want to go.
However, I now send all of my customer service requests directly to the social team because they do a phenomenal job and typically respond within an hour. You can reach the team here: QVCSocialTeam@qvc.com.