Is there a way to view the Websocket traffic?
Only Websocket headers are visible on the initial handshake.
Everything disappears after the response:
The current version of Fiddler works just fine with WebSocket traffic. See http://blogs.msdn.com/b/fiddler/archive/2011/11/22/fiddler-and-websockets.aspx
See http://blogs.telerik.com/fiddler/posts/13-06-04/what-s-new-in-fiddler-2-4-4-5 for how to put the data on the Log tab.
To display data on a WebSockets tab,

you need an extension (this is slated to be built-in for version 2.5). For now, you can grab the current bits. Simply extract the ZIP and put the two files into the \Fiddler2\Scripts folder and restart Fiddler. If you double-click on a WebSocket session in Fiddler’s WebSessions list, the WebSockets tab will appear