I personally think it's your router. I have never had this issue and don't see why you would either other than you having a bad router.

the only other suggestion i can make is to manually assign ip addresses to both consoles, it could be an issue with that. When you manually assign their ip addresses make sure to leave a bit of a gap between them for example.

your xbox - 192.168.0.25

brothers xbox - 192.168.0.50

as long as you arent connecting an extremely large amount of devices this could help.

If not its probably as suggested, your router, if you are a Virgin user and you recently upgraded your internet to the 100 mBs connection then did they also send you the superfast home Hub? its generally a different hub than a standard Hub, The older hubs cant handle the faster connection speeds and boot devices, i had this same issue with mine but it was with my PC and console connecting.

If you do have the new Hub you can try doing a software Update, setting one console as the DMZ, or forwarding all ports for xbox live.

Give this a go and see if it helps

in my house we have 2 Xbox ones and a PS4 all can connect at the same time no issues.

GV

GT-R wrote I personally think it's your router. I have never had this issue and don't see why you would either other than you having a bad router.

I told him the same thing. Had the same issue on xbox 360. Had my friend bring his router over, same exact one and none of our xbox's got disconnected then so i returned the one i had.