This may not help many here, since it relates to firewall rules rather then any gateway rebooting problem.
I had successfully activated a TTN gateway at home and then took it to another location where a device running m0n0wall firewall software generally limited traffic except to specified permitted ports or IP addresses.
I did the five second reset button push, after first powering on, to clear the previous, locked activation.
And when I tried to then to activate the device, the process stalled with one steady light plus one blinking light (i.e., checking for Internet) on the gateway. That was fixed when I opened outgoing access via the LAN to all UDP ports. When I tried to just add UDP access to destination port 1700 that didn’t seem to fix the problem for purposes of initial device activation.
At that point, the first three LEDs became steadily lit, with the fourth one blinking (i.e., gateway not successfully connecting to router). That was fixed when I opened up TCP access from the LAN to destination port 1883 in order to permit MQTT communication, as per the instruction here: http://www.hivemq.com/blog/mqtt-security-fundamentals-securing-mqtt-systems.
Then the activation completed successfully, and I was able to send traffic via the gateway using a TTN node.
I’m no longer at that location, but wonder if I could have further limited the outgoing UDP traffic after the activation was complete.