console losing Internet connection

If your signed in and lose internet connection it will sign you out.

As far as it telling you that you do not own the games.

In order to prevent that from happening that console would need to be set as your home console if you are not going to be connected to the internet. Yes I know you are losing connection but if you are wanting to play games offline that console would have
to either be set as your home console or you would have to put the console into offline mode before going offline.

If you are getting an 8 digit error code when you are disconnected please post it for more assistance.

I'd try rebooting your network hardware and assigning a static IP address via your network hardware and NOT the 360's Network Settings. Usually you can set it using the 360's MAC in your router's settings. Assign it to something not used by any devices on
your network:

(MAC address)

Local IP: (e.g.) 192.168.1.120 (Mine for example)

My console has been doing the same thing since whatever it was that happened around the first of April. The status page says things are working, but whenever I try to use one of the media apps or a play a game I get DC'd. If I do stay connected something
like Youtube or Netflix runs very sluggish and then finally boots me.

Also support's suggestion was to send it in for repair, so that's also effecting my decision to think my console has the problem.