This is odd indeed.
After a power failure I would expect the obi to keep trying to to obtain an IP untill successful. Such is the behavior with firmware 3.1.1 (Build: 5462EX). The obi has other dhcp issues, but those are not relevant here as your until is coming back up from a power off state.
My set up here is far more complicated, involving a hardware firewall/router, wifi ap's, switches, etc. It literally takes upwards of 4-5 minutes for the network connectivity to be fully reestablished after a total powerloss/shutdown.
In general, firmware updates are not preferred unless they fix a specific issue i'm having. Many times you end up with other functions getting broken (albeit operational dhcp is vital to network access). I know there are newer builds than what I have, but it works fine. When it stops (or google makes changes) then I'll consider updating.
A ups will help, but how much? I have a cyberpower 1350 connected to my network parts (modem, ap, firewall, a switch, and the obi). According to the status page everything consumes ~40 watts resulting in estimated battery runtime of about 90 minutes. Great for a brief outage but not for one lasting 2hrs + (happens on occasion in this area). Say the typical set up with a modem, router and obi will give you 2 1/2 hours. Still, once battery is exhausted, everything will shut down. Instead, I configured everything to shutdown after a certain amount of time (haven't settled on a good number yet, probably 15 minutes). Once power is restored, everything boots backup.