Data centres, business, hospitals etc. run batteries to bridge the gap until the diesel starts running. It can take a minute or a few until the diesel generator takes over, but it can run for hours and days with refuelling.
Getting batteries for 8h is expensive and risky - what if the power cut suddenly lasts 9h? With batteries you have a fixed storage, with petrol or diesel you can just refuel.
Having that unreliable electricity, my home server would be the least of my problems. I would already have a generator to keep the fridge running so the food doesn't go bad every other day.