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I have a tank that suffers quickly (4' high but only about 16" around, no exposed return and little surface area) if the air pump is out. I keep a Penn-Plax battery backup (the one you plug in, not just a battery operated one) attached to that system. When the power goes out, the air pump turns on and runs off the standard "D" cell batteries but it does not act as the air pump under normal conditions (ie, I have a separate electric air pump on the system for day to day usage). They are pricey but it looks like they have at least come out with one that looks nicer than my blue box. I have found it to be totally reliable and the batteries last for years (and because they use "D" cells it will run for a long time). The biggest problem is remembering to check to be sure the batteries have not died from old age.
For the octo tanks, I keep several battery operated pumps in the house and the few times the power has been out for over an hour, I set these up. I would really like to have the automatic backup (or what I would really like is a generator for that room) on all the tanks but I thought them expensive at $26 and it looks like have have gone up to about $50 (with shipping) now.
I don't think the B10 is a plug in/auto switched unit but the B11 definitely is and found it at the $21ish price I paid for mine while I was checking the models. These are back up only pumps that last a long time (unlike some of the really inexpensive ones) and the D cells run for more than a day. They are noisey (forget the "Silent" in the name) but I can live with that as long as they always work and they do. Mine is over 5 years old and still works like a champ.
I believe they do make one that is designed to run full time AND has a battery backup and that may have been the ones I initially found in the $50 range.