I wash them in the dishwasher and they come out clean,
but once in the basement again, after a few months,
you notice that the same ones have mold. And the rest
never get mold.

I'm wondering whether it's plasticizer migrating to the surface.

You might try putting the "susceptible" items in plastic bags and sealing them
tightly. I wouldn't be surprised if the "mold" continues to form.