Just how robust are those back-ups? Back-up systems have a limited duration. They are designed to be on-line until normal power is restored. If the grid is down long-term other arrangements will need to be made.
The obvious limitation is fuel supply to the generators. But chances are pretty good that it's a long-enough supply to continue pumping until decay heat levels drop.
A good design would then implement natural circulation or some other relatively passive means to dissipate the decay heat after the pumps are stopped.
But if you could get diesel fuel to the site continuously, then you could run the generators continuously (until they break).