UPnP that the symbols you refer to is a pile of rubbish and generally best avoided for router management/availability tracking.
The router reconnecting to ADSL should not result in the PC renewing its IP address allocation, so while the internet may go, it should still be able to see the router. That is unless it is one of the not so good routers, that totally crashes and the reconnects are down to it restarting. On a PC it would be called the Blue Screen of Death.
NOTE: Is this wireless or ethernet we are talking about?
My Win 7 netbook moves between various wired/wireless networks without any need for reboots.