Which is why most of us recommend setting DHCP reservations for the Tablo, so it won’t stop working while you are away and you get a new IP address. Without DHCP reservations, there is no way to ensure the Table will get the same IP back, but in theory it should. With DHCP reservations, it WILL.
DHCP reservations are for internal IP assignments of devices. Even with DHCP reservations rebooting your router will result in a new External IP which requires you re-pair the device. Internal IP and External IP are different.
The issue here is external IP change.
But the Tablo WILL still need to be connected to the internal lan, or it will not connect. If I reboot my router (but not cable modem) I should keep the same external IP. I have a stand alone cable modem, and router. Two different companies. I can upgrade one, without the other.
That is not correct. When you reboot the router only it re-negotiates a connection with your ISP and your external IP will change even if the modem is not power cycled.
This is why I said my external IP changes if I reboot the router or the modem - not both.