I have seen this issue before if it's what I think it is. What goes wrong is a network issue since you use the same internet connection where your network only successfully routes the almost identical traffic to the two consoles to a single console.
First thing I would try would be to:
- Power off the consoles and remove their power cables.
- Find your router (and other network equipment) and remove the power as well and wait 5 minutes.
- Power all the devices back on and see if it works.
If the above do not work can you describe your network setup? Also do you have access to your router?
