When you close IE there used to be an option that says disconnect when i close the internet, you must have set it as don't show me this message again whilst clicking yes. Not sure how to sort it though.
Something is probably set to check if your internet connection is active (it could be software on your PC, or it could be something set up at the ISP's end), and whatever it is probably only cares about port 80, which is used for the web, or something like that. It's probably ignoring the SimSig traffic.
You could open something like a Live Departure Board page and set it to refresh every 2 minutes, that would do it, if nothing else will.
BTW See the 'SimSig next play' topic under 'SimSig & other sims' if you wish to join us in our online games.