Not sure where, but a year or two ago I remember reading that a power outage could destroy all your bacteria if anything over 5 or 6 hours or something. Glad that's not the case.
You probably read it here many times. Too many factors involved and too many unknowns about the bacteria themselves for anyone to make a statement like that. What is known is that the bacteria need oxygen and a nitrogen food source ( ammonia, etc). As long as those are present, no reason they should die off. In a closed filter like a cannister, they'd run out of oxygen sooner than an open filter like a HOB, but no one can say for sure how many days, or hours. Anything you read is speculative including my own opinions here. IME once established, they're pretty hardy and don't die off as easily as sometimes portrayed. Just my experience.
I had a small tank one time that was giving me fits with nitrite levels that just wouldn't go away. Finally I noticed that the last time I had messed with the filter (2 weeks prior ) I had forgotten to plug it back in, doh!
. Plugged it in and the next day nitrite was 0 and stayed there. The little buggers were still alive and well and working just not on my tank water since it wasn't flowing through the filter. There'll still be some oxygen/carbon dioxide exchange going on at the surface of the filter water that'd keep some alive.
If anaerobic conditions existed in the water as well, then you may end up with the nitrate being converted back to nitrite which is why it's a good idea to dump the filter water and refill before turning it back on. If only off for a day, there's not enough time for that process to happen to any extent, but you could replace the water just to be safe.
One other note. For some reason the bacteria seem less hardy in the early going. I'm not sure if it's a numbers thing or type. There may be many types of nitrifying bacteria, and the ones that are present in a long established filter may be hardier than what's present in the early going. But, again, just speculating based on my experiences.