I second the success reports of HAProxy 1.5dev with SSL support. It's been stable for me over the last month, and more performant than using STunnel for SSL, which is what I'd been using for the last 1.5 years with Websockets. HAProxy is a remarkable, wicked fast, and very stable product.
In the whole of my DevOps career, getting SSL working with web sockets was one of the most frustrating.