With the sketch serving up the complex webpages I get the "waiting for a response" in the browser - or whirly wheel as you call it. When GETs receive no response, random parts of the webpage, images etc are never rendered.
I've looked at what is going on with a HTTP Debugger and could see that some GETs were never getting a response. I also noticed that if I could make sure the GETs didn't overlap everything works fine. For example, Firefox is well behaved and usually sends its GETs consecutively. IE 9 sends GETs which often overlap in time.
My sketch never freezes or completely stops responding. It is just when more than one GET arrives at the same time, one of the GETs doesn't get processed and there is no response.
cheers