The Xenoblade wiki mentions "Should the countdown reach 0 before another power source is installed..." but as far as I recall, no one ever mentions that they're carrying anything of the sort in Ch12, and when Elma is fixing it, she just types on the terminal for a bit and ta-da, power-wise everything is okay again.
The way I understood it as a played through it was just like you said, that there was some sort of backup-backup power system, but no one in their right mind builds some contrived shit like that where someone has to activate that manually.