It will really depend on the size of your tank, and the season. Large tanks will hold their heat for quite a long time, and tropical fish can quite easily survive substantial temperature drops, as long they are slow, over a long period. My 160 litre tanks can go 36 hours without heating before the temps drop too low, and my 400 litre tank can go several days, in winter. Morning temps in the house in winter can go as low as 2C here. In summer, the heaters almost never click on, as our summer temps can get over 30C.
Remember, your tank temps won't really drop below the ambient air temp.
If you have smaller tanks, or the power cuts are particularly long, and it is winter, there are a couple of things you can do. With my 20 litre and 30 litre betta tanks, I wrap them in bubble wrap, and then wrap a towel around that. This will keep the heat in for quite a while. The other thing you can do is use small empty soda bottles, or jars, fill them with hot water, and drop those into the tank. If you use jars, make sure they have plastic lids, not metal ones. The heat will slowly dissipate into the tank, keeping it warm. Don't overdo it though, or your tank will heat up too much. Just keep an eye on the thermometer. I sometimes have to use this method if we have particularly long power cuts because the lines are down from a storm.
Hope some of this helps.