Router rebooting

You don't refer to which gateway/router you have. T-Mobile has the Nokia, Arcadyan, & Sagemcon gateways. I have seen a couple of reports of behavior like you refer to recently. It might be related to a bad power adapter, software issue, or a internal electronic problem on the board. It is hard to say for sure. 

Not knowing about the steps taken when you obtain the gateway and set it up it is hard to say for sure. While watching one of Nater Tater's videos he made a very good point about the initial setup of the gateway. Since T-Mobile pushes out the firmware updates as they do it might be related. He suggested to plug in the gateway and allow it to stand idle for a bit of time prior to doing the initial configuration and setup of the local wireless network so in the event a firmware push was made and loaded it would NOT be interrupted in the middle of the progress by accident. With the Nokia gateway the small LED screen is on the top of the gateway so it is hard to keep up with what is taking place on that one. With the Arcadyan and Sagemcon they have the LED display on the front of the gateway but I do not have one of those so when a firmware push is made I do not know if it posts a warning or notification that the device is in the process of updating and to not interrupt the progress of the upgrade. 

Given there may not be an official T-Mobile statement about this possible situation upon the initial setup process I suppose it is possible to stumble into the problem. If the gateway does take a firmware push and is in the middle of an update and it is interrupted at a critical point by a power cycle there could be corruption and result in the gateway being able to recover and boot to a functional state. It may be there are proper checks in place for recovery but maybe not. Just speculating as to how it might get into such a state IF there is/was no hardware failure. 

So, there are probably a few possible ways the gateway could get into that state but without being able to debug the device it is not going to be clear. I think your best bet is to take it to a local T-Mobile store and request a replacement. Then when you get a replacement home just power it up and allow it to stand for a period of time or say 2-3 hours. It would probably be safe to check the initial state for the firmware revision and record that and then after a bit of time check it again. If the firmware did update then leaving it set so it can load the newer firmware is probably a good thing. When Nater Tater was doing his video with the Sagemcon he was reporting on it was a brief time before it did report the firmware update was started. He waited for that to complete before proceeding and that was when he made the reference to watch for that and not to interrupt the process. 

Just a theory but it is possible it might be related.