I've purchased a few of them from REI Garage Sales with rips through the seat material. There a few brands/models I've found easier to sew/replace the fabric as the metal/plastic frames aren't needing anything.

So far my favorite is the Alps Mountaineering Camber chair. The fabric is held on by Phillips screws.

As to your specific predicament, it sounds like you aren't letting your stuff dry out and keeping it dry. Camping chairs last me a good five years and usually degrade from UV exposure. I've never had one rot from mold.