Caudal fin deterioration is most likely either caused by nipping by another fish or by environmental conditions; the latter is the cause of fin rot, and then fungus.
Have you observed any fish ever approaching the corys from behind as if to possibly nip? The best way to look for this is to sit motionless in front of the tank for up to an hour. And I mean motionless. The fish will forget you are there, and you may observe more natural behaviours. When we are present, fish often associate us with food, and will be thinking of that and not other things. This is not as far fetched as it sounds.
As to the environment, what are your water parameters (GH or general hardness, pH, and temperature)? And have you tested for ammonia, nitrite and nitrate?
What size is the tank? What is the substrate? Is there plenty of hiding spots for the corys, such as plants, chunks of wood, caves, etc?
What is your water change schedule (volume and frequency)? And what substances/additives are being added to the water (water conditioner, and any others)?
Lots of questions, but pinning down a problem requires us knowing all the facts.