I have had salt in with my corys before. I was treating for ich, and followed the guidelines here in the forums, so yes, it was a gradual change, and I also raised the temp up several degrees. Kept it that way for a few weeks, until I was certain the ich was gone, then returned to normal (un-salted) water changes. Had 3 corys that made it through all of that.
A month or two later, one of the corys, the smallest, appeared to get sick, presenting the same symptoms as yours, Rockbellab; the fins laying flat against them, and finally he just laid on his side, looking like he was gasping for a breath. He didn't make it of course, but the other 2 have been just fine.
I love my corys, they are very adorable, and just a BLAST to watch!! I would definately not keep one by himself for very long, he needs friends!! They follow each other all over the tank, and I'm pretty sure that mine would be lost without each other. Sometimes, it's like they're playing some sort of mimmickry game, or simon says or something.
I wish you both the best of luck with your corys!!!