You shouldn't be digging and dividing peonies until September. Apart from that I do know they can have problems with nematodes, you might check to see if that could apply here.

I don't want to divide it, I need to re-locate it. I know it's not an ideal time, but we get frost in September (Alaska), so I need time to remove all the plants from the site, build raised borders, fill in the bed, and re-plant everything. I have to start now or they will sit in a pool of melted snow again next year.

Only thing you can do is dig out as much of the rot as possible, apply fungicide, powdered seems to last longer on the root, allow to dry and replant. If the plant has been in that area for a number of years this happens naturally especially in the older cultivars. Back in October 2011 one of the members on here posted pictures of the root from a plant that had been in the ground for years perhaps even 100 that after this stuff was rinsed out it was hollow but still alive. I asked last year if the divisions that were made lived but they did not.

If you are only planting for your own enjoyment and not commercial usage I would not attempt to divide but just plant back.

One of those ???? things. If older 50+ in the same spot are still alive and appear to be thriving with what appears to be rot on the inside does the stuff on the inside provide nourishment to the plant. I think that some how it does because if it was just rot the plant would die.