It entirely depends on your set-up, species of fish, size of tank, stocking levels, ventilation of the room, temperature of the room etc. how long a particular tropical fish can survive without a filter or heater.
If you've got discus, probably not long, although I did hear of a discus breeder who's fish were fine after an 8 hour power outage (he didn't feed them and did several water changes with RO). If you've got goldfish, possibly months before they finally succumbed. People have rescued bettas from the bottom of a rotten lily vase and they've survived.
Planted tanks would probably survive longer, provided there was a light source, as plant excrete oxygen and use up ammonia.
So, there isn't an easy answer. I personally don't like to have my filters out of the water for longer than 20 minutes, less if I can help it, and I wouldn't have the power out for longer than half an hour at most. However, the oxygen levels and ammonia levels in my tank would probably be fine. I recently had a 4 hour power outage and even my heavily stocked tank with delicate fish was absolutely fine.