I had a somewhat similar puzzling experience like that a few years ago in my basement too. Metal would rust very quickly in one particular area that was primarily used for storage of paint/stain/caulking stuff, and some other misc. stuff, and I knew it wasn't a humidity problem. I finally figured out that it was coming from a half full jug of muriatic acid. The jug was completely intact and the screw cap was on tight, but aparently the fumes somehow were getting out and causing the reaction. Look around to see if there is any chemicals or strong cleaners in the area that may be the source of your problem. Good luck.
JR