I haven't fiddled around with server push yet.
However, http://ajaxpatterns.org/HTTP_Streaming might be useful to you.

I'd guess firefox simply fed up waiting for the finish of the response.
Perhaps you should add something like body.onload="window.location.reload()";

As far as I know you can't rely on a persistent connection.
Besides the IE, who will break the connection in each case, the client could loose the internet connection for example.

I'm however very interested in http streaming, could you perhaps msg me how you solved the problem ?
michael