Following an apparent User Interface change on Norton 360, I’m also getting same message claiming I’m on a public network (it’s private), and the VPN works for about 40-50 seconds and always disconnects. It reconnects, then same disconnect. Frustrating. VPN worked fine and was steady before something changed.
So I don’t know if my answer is off the mark but the old N360 version had three Network settings–public, private and restricted. The new version did away with Restricted so your choice is Public or Private. Have you checked what your network setting is? I noticed that when the new version of N360 installed, it randomly changed my network settings on all of my computers. Even though all of them had the same setting before the install, each computer ended up with a different setting. Go figure!
Go to Security>Advanced>Smart Firewall>Network in N360 to verify your setting or to change it. You’ll need Admin privileges to do that, of course.