It isn't just the lack of food - it's the lack of essential oxygen as well. Without anything left to cause surface aggitation and therefor gas exchange, and with a temperature fluctuation (though warm water changes can solve this to some extent though obviously isn't a long term solution), the bacteria can die rather quickly. Usualy, however, enough survive to catch up on the cycle quickly once the power's back and regular water changes while this (the re-cycling) is happening will keep the fish alive - but if there's a power cut and the temperature drops dramaticaly, the fish can die almost instantly (especialy in smaller tanks where the heat is lost much quicker).