This is expected behavior. If the ADSL router is still powered on and more or less working, NetworkManager will still show as connected because it is still "connected" to a physical device, which appears to be there -- in other words, there is still electricity going through the cable, even if the internet connection may be down.
** Changed in: network-manager (Ubuntu) Status: New => Won't Fix -- You received this bug notification because you are a member of Ubuntu Bugs, which is subscribed to Ubuntu. https://bugs.launchpad.net/bugs/753068 Title: Network icon inaccurate when displaying connection status -- ubuntu-bugs mailing list ubuntu-bugs@lists.ubuntu.com https://lists.ubuntu.com/mailman/listinfo/ubuntu-bugs