If your fish are breathing heavy and not eating, there's something going on, either the fish are sick or the water is not good. Maybe one of the parameters has slipped out of range, it could be the temperature, ammonia, nitrite, pH, anything of those things will cause stress on the environment and cause the fish's immune system to be suppressed. When there's something wrong and the fish are stressed, the first thing they do is they don't eat. A lot of times they breathe heavy. If there's a parasite that's affecting their gills, they're going to breathe very heavily. If they're being chases around, if there's an aggressive tankmate, they're going to breathe heavy.
Fish should have a very unlabored breathing. It should be very steady. Without being a marine biologist, you should be able to recognize normal breathing versus heavy breathing. If the air pump stopped working or the filter which provides the oxygen for your particular aquarium has slowed down, maybe the oxygen levels are low, maybe the tank is too stocked. The fish have grown over the last 6 months and now there's not enough oxygen for the amount of fish that you have, so the fish are breathing heavy. If there's nitrites in the water, that prevents the fish's blood from carrying oxygen, so you should test your nitrites and see if they're elevated. All of these things will result in a fish being stressed if they're breathing heavy. If they're breathing heavy, you want to make sure that the water chemistry is good, they're not being chased, they're not suffering from any ailments, make sure they don't ick on them, and try to get their breathing to go to a normal rate.