There is no such thing as connection on server side and/or browser side. There is only one connection. If one of the sides closes it, then it is closed (and you cannot push data to a connection that is closed obviously).
Now a browser closes the connection when you leave the page (it does not depend on the library/language/OS you are using on the sever-side). This is at least true for WebSockets (it might not be true for long polling because of keep-alive
but hopefuly socket.io handles this correctly).
If a problem like this happens, then I'm pretty sure that there's a bug in your own code (on the server side). Possibly you are stacking some event handlers where you should not.