What happens inside a stopped filter
A filter colony is an aerobic workforce: the bacteria that process ammonia and nitrite need a constant flow of oxygenated water across the media, plus the waste stream that feeds them. When the power stops, the flow stops. The bacteria keep consuming the oxygen trapped in the canister or chamber, and once it is gone they begin to die back — fastest in a warm, tightly sealed canister, slowest in media that stays wet with some air around it, such as a trickling sump or a sponge sitting in the tank itself.
The honest timescales
In a warm sealed filter, measurable die-back begins within a few hours, and by around a day without power a colony is typically much reduced — though rarely wiped out completely if the media stayed wet. Media that dried out entirely fares far worse than media kept submerged, and a cool filter outlasts a warm one because the bacteria's oxygen demand falls with the temperature. Treat any precise hour-count with suspicion: tank size, stocking, filter volume, and room temperature all move the answer, which is why the safe plan assumes damage and then tests to find out how much.
While the power is out
Resist opening a canister filter repeatedly; if the outage looks long, the colony's best chance is media kept wet and given air — moving media into the tank itself, or into a bucket of tank water with a battery air pump if you have one, gives it both. Do not feed the fish during the outage: uneaten food and extra waste load water that nothing is currently filtering. Keep the tank covered and undisturbed, and remember the fish face the same falling oxygen as the bacteria — a battery air pump run in the tank helps both.
Restarting without finishing the colony off
When power returns, let the filter run, but do not rinse the media under the tap to clean it — chlorine in tap water will kill more of the colony than the outage did, and any rinsing should be in removed tank water only. Expect the tank to behave like a partial re-cycle: test ammonia and nitrite daily for at least a week, feed lightly, and cover any spike with partial water changes using dechlorinated, temperature-matched water. Fish showing gasping or clamped fins during this period need a water change first and questions later.
Planning for the next cut
A cheap battery air pump, and knowing where your media can be moved in the dark, turn the next outage from a colony emergency into an inconvenience. When that choice is unclear mid-outage, put a follow-up question to KinsLe's Kinny; he answers using the KinsLe Answers library.