Since it sounds like it has a regular cycle, you might take a look at your routine and see if there is a part of your routine that cycles the same way.
You could take general precautions to prevent and control contagion, as well. Of course, keep the ill sepparate from the well. I would set up a quarentine room, and clean and disinfect the whole house. Wash your hands after every time you handle one of your kitties, and use latex/vinyl gloves when handling them and their waste. Remove your shoes when you come in from outside and spray them with Lysol, inside and out. You may even keep a set of "sick clothes" that you change into to handle your sick babies. Basically, do like they do in the hospital with MRSA.

I know you said they did blood tests, but have they checked for parasites? I would imagine there are some, that during their lifecycle, would cause systematic issues and irritations.

Good luck and we'll keep you in our prayers