If the fish that you started with are becoming unhealthy, then they are either sick or starving. The original fish can live indefinitely as long as they are properly cared for. Check the two "meters" in the lower right corner just below the tank while one of your fish is in the isolation tank or while you are holding it. The top meter displays the fish's current health, and the bottom meter displays how well fed the fish is. When the bottom meter turns yellow, it's time to feed the fishies. If the Fed Meter is red or (yikes) totally white, your fish are starving.

To determine if a fish is sick, just grab it and look at that black area above "Your Cash." If your fish is sick, you will see the word "Sick" in that display area. You should either cure the fish or trash it, since disease can spread among your fish population. A description of each type of disease can be found by clicking on the two different treatments in the Supplies Shop.