I can tell you that after two hurricanes I've learned a little bit. I have two APC 1400va UPS, that I keep charged and run the main pump (mag24) on one until it dies, roughly 2-3 hours. The other I hold over for a MJ1200 that lasts 3-4 hours, amazingly the difference is pretty small between two vastly different pumps. I do have a 6000 watt generator, so every 3-4 hours I run it and recharge the UPS, so it does save me a little run time and gas.
I used a battery powered air pump during the last outage, it died after 4 days without power (not dead batteries, it just croaked). My advice is the battery air pumps, they're cheap so get a few of them. I went through one battery change in the four days before mine died. Maybe I just got a junk pump, I don't know.
The alternate idea I'm looking at now is a few golf cart batteries and a charge inverter for more runtime. I suspect I can run 12+ hours with four batteries and a 500 watt inverter, then run the generator to recharge when needed. The main thing with any battery on inverter or UPS is not to decharge past 80%, better if not more than 50% or you severely shorten the life of the battery. I suspect my UPS were pretty degraded when I got them from where I work, hence the short runtime.
Hope some of that helps. Everything can live without light for several days, without O2/circulation for several hours. There really isn't a reasonably priced UPS that would run much for several days, even with a REALLY small powerhead.