Theoretically, the beneficial bacteria start dying off after about 30 minutes without oxygen (oxygen is supplied to them through filtration, so when filter is off, they have no oxygen). But, I've had my tank without electricity for at least 24 hours during a power outage. And nothing bad happened to my fish. I measured
ammonia and
nitrite after the power outage and they were at 0, so that means I didn't loose my nitrifying bacteria. Or if I lost them, I didn't loose enough to cause a mini-cycle.
Also, it's better if the power outage happens to be in the summer because then tank water temperature can be warm without a heater. But in the winter, the temp. of a tank can be too low without heating in your house (since your tank heater is not working during a power outage).