The boards are applied vertically, yes? I have a 1/4-inch finish stapler and have found the staples too smooth (and thin= slippery) to hold exterior boards well.
I'm guessing a large reason these staples pulled is that 3/8 is a thin substrate for any fastener to bite to. Screws would help, as would a ring-shanked nail. But again that OSB is thin. (And OSB is kind of lousy no matter how thick).
If I was starting fresh, I might glue and screw some horizontal furring strips @ 16" O.C. down first w/ waterproof polyethelyne construction adhesive. Apply the boards over this w/ a ring-shanked nail.
A quick-fix in your situation would be screws, I guess.
