Xbox controller/lose internet connection

I know why my internet keeps disconnecting. What im saying is my controller disconnects when i lose connection. It will reconnect but on rare occasions it will not turn back on. Dont worry about the wifi part. All I need to know is if the controllers are
supposed to drop conneection and then reconnect when the xbox all of a sudden loses internet connection. I dont lose control of the wifi.

Thanks for this info, that explains everything now!

the fact is xbox has this bug lately with kicking people off the internet. The problem is that they are doing their best to fix the accounts that need to be banned. So when they do that they reboot the server globally so everytime they update their server the connection gets lost. Just go with the flow for now until they are satisfied with the banned accounts.

Mine did the same thing when I first got it. It remedied itself for me, because it hasn't done it for awhile now. I'm not sure if it was an update or what it was. Maybe try Uninstalling the updates, and try re-downloading everything and see if that helps?
I recall doing a system reset, so maybe it was that. It's been months tho, so I can't remember off the top of my head.

What version of the Xbox do you have? Is it possible you are connecting wirelessly and wired at the same time? This would create a network loop.

Additionally, it almost seems like an IP conflict. You don't have an IP hard coded on your Xbox that might fall into your new routers DHCP range, do you?