Fluorescent lighting is just as bad as sunlight for fading dyes. I really need to make some kind of covers for my plastic bins to keep the light off of them.
I've never stored fabric in sunlight, but I opened up a yard of fabric the other day to turn into bias binding and the top layer was bleached out, in exactly the right area to make the whole piece unusable for the binding. :(
So many of us are using compact fluorescent bulbs, these days - and they're really terrible on art and textiles.