|Can't really make a good guess without having hands on experience with the hardware being used, but here's a couple of mediocre guesses:|
1) If part of the procedure you go through when you manually get the router to reconnect is to make configuration changes to the router's settings, then perhaps your not saving them when you finish. That is, you are making some kind of change in a system menu and activating the change, but that change doesn't get saved in the flash memory (it's just in the RAM), so when the power goes out the router reboots with the same settings it had before you made that change.
2) When the power goes out, both, the router and the modem go dead. When the power comes back, maybe the router boots faster than the modem and doesn't get automatically configured. That is, the router is pinging the modem for the configuration info, but the modem isn't ready to provide it. By the time the modem comes up, the router has given up and remains unconfigured. This is why it would be a good idea to plug both of these units into a UPS if you decide to go that route.