The default value for Line Port -> LineInUseVoltageThreshold is 25 -- I'm guessing that when on battery, the ONT supplies less than that, so the OBi thought the line was in use and wouldn't connect the call. Test by removing AC power from the ONT and checking the OBi's Line Port Status -> TipRingVoltage. If desired, set LineInUseVoltageThreshold to a few volts less.
Alternatively, for the Phone port, set EnableLINEPortBargeIn, which will allow # to connect to the Line port at any time.
Of course, the best solution would be to feed the ONT with protected power, but I've heard that VZ often makes that difficult by installing it e.g. in the garage.
I don't have FiOS, but have two systems that are somewhat similar. One is AT&T U-Verse. Though far inferior to FiOS in most other respects, they do provide a beefy battery that can power the entire iNID for several hours. The other is Orange FTTH. They have no battery backup at all, but run fiber as needed to put the ONT right next to your router, so it's easy to supply it with protected power.