I'm sorry that I don't think I can be of much help other than to empathise.
I had pygmy cories, all of which died between months 6-9 in my tank, of similar problems to what you describe but additionally other problems (including partially-/fully-severed tails, pus-like lumps and bloodstreaks under their pelvic/anal fins), despite water parameters being in line with their requirements, water quality being consistently 0 for ammonia and nitrite, and 20 for nitrates and despite a varied diet. All other inhabitants were fine - initially x-ray tetras, then also harlequin rasboras. Having exhausted all obvious options, I've put mine down to either:
*the tank being insufficiently mature when I got them (not long finished cycling although it didn't pose a problem during the first 6 months of them in the tank);
*being harassed or feeling intimidated by larger tankmates (in particular two female tetras who lurked around them, waiting for food debris being foraged, although there was no sign of them being perturbed and they were quite happy foraging in dispersed locations around the tank rather than in groups or hiding);
*6 (but dwindling in numbers) being an insufficient number .v. the size of their tankmates
Might any of these be a possibility? [Here are a couple of useful profiles for the sterbai cory - perhaps an additional few might help? Are your water parameters suitable for them?
http://www.thinkfish.co.uk/fish/sterbai-cory.html and
http://www.seriouslyfish.com/species/corydoras-sterbai/]
Mine didn't respond well to the eSHa 2000, and, in retrospect, I wished I'd dosed lower than suggested, particularly as they were so tiny. On that basis, although yours are bigger in stature, I'd err on the side of underdosing any medication you try.
Best of luck, and sorry I can't be of any more help.