You experience this behavior if your router or the gateway is incompatible with Xbox Live, or if your router or the gateway has an incorrect MTU setting.
This test confirms that the network has sufficient Maximum Transmission Unit (MTU). MTU is a setting on the router or the gateway that can affect network performance. Xbox Live requires a minimum MTU setting of 1364. If your console does not pass this test, you cannot sign in to Xbox Live.
If you have multiple consoles that are connected by using the same connection, you may cause a failed MTU tests. A failed MTU test may also be caused by sharing the connection with a computer.