I'm no expert but the Cory's most likely aren't the problem, I have five in my tank and they are very active. If I had to guess I would say that your Nitrates being so high are what is causing the problem.
Is it a BB tank or a display with substrate?
I would suggest getting aggressive with the water changes if you are certain your tank/filter is cycled. I ran into the same issue and was doing a 50% water change once or twice a day until the nitrates became stable.