Someone posted here, a while back, that you can dig out the dead center, fill it with new soil, and the healthy perimeter will fill it in. I've never tried it, but it seems logical.

When my centers die out, I dig up the whole plant, and take divisions from the perimeter. If your plant is too big for its neighbors, this might be the best bet. Dig out the entire crown, and replace it with a smaller healthier piece from the exterior of the crown.

Either way, it's important to take out the old dead part of the crown and replace it with good soil.