So I have run into the same exact issue! And delved into the world of Networking issues to no avail. Along with the following Things That Did Not Work:
-Exiting out game Reset Xbox
-Reset router
-Reset gateway for router
-Reset router to factory settings
-Reset to factory defaults on Xbox
-Setting Xbox to Static IP address, (thinking this would help).
-Enabled Port Forwarding on for ports TCP & USP 53, TCP & UDP 3074, TCP 80, and UDP 88.
-Enabled UPnP
-DMZ on with port forwarding off
-Reset Xbox software by clearing cache and reinstalling update.
-Calling Comcast and having them do the same resets and changing router channel.
-Port triggering for the ports mentioned above when more than one Xbox is in use, port forwarding off, DMZ off
-Wiring the Ethernet cord to each device
-Another multiple resets
-More resets...
I'm also trying to use multiple consoles, we have 2 Xbox360's in our house, however this issue occurs even when only one of us is on. I'm going to try to set up what you said before ultimately getting another router.
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Are you using the router they provided?