I totally agree with Prism 99 (love that name by the way), I would applique squares over the deteriorating squares, as it looks like it's the same fabric that is deteriorating, then quilt over them. I think they are a treasure and I would at least try to repair them, by appliqueing squares and using fusible interfacing to repair the rough patches. Then I would suggest soaking them in the tub, gently agitate them, squeeze as much water as possible out and then I would spread them out on a sheet in a shady area of your lawn to dry. I have used the applique method to repair a quilt I'd made, the first one I did on commission, where some of the black fabric developed small holes. Since it was a Roman Stripe Quilt, I appliqued the black triangles on, then quilted over them, following the SID of the other blocks. What a treasure you have and I would try to keep them in the family.