How to move several terabytes of files with an unstable NFS connection?

How to move several terabytes of files with an unstable NFS connection?

I have inherited a proprietary, distributed storage system that exposes its files through NFS. I need to move these files off the system. The trouble is that NFS links are reported as stale before I can list -- let along move -- even a modest fraction of the files. Current solution is to restart the NFS client every time a call to cp -aur * fails, but that is gets very inefficient as the number of files already copied grows.