There is unfortunately sometimes a chain effect. One fish dies of random natural causes, and his corpse causes an ammonia spike, which causes damage to another fish that eventually dies from the accute poisoning, and his corpse causes an ammonia spike...
Clamped fins is a sign of stress, often of ammonia stress. Unless you can find some other symptoms to go after, I'd diagnose it as a chain effect of stressful situations in a tank with a full bioload.
Wait for things to stabilize, and then consider upgrading your biological filtration before bringing the tank back up to full capcity. Deeper gravel, additional filter, more media in existing filter, addition of live plants, whichever works for you. You had a pretty reasonable bioload before the babies were born, but if you're going to continue to breed you need a bit of a reserve for them.
You might also consider getting some plain old pond snails. My snails not only pick up waste bits of food and clean my glass, but they cluster densely around corpses and make them easier to find quickly.
If you notice any other symptoms, either physical or behavioral, be sure to let us know so we can look at any other possible causes with you.
Make sure to QT all new fish before adding them to your main tank with the survivors.
The Freshwater Quarantine Tank