I've just experienced an instance of the Synology NAS (DS411j) NFS file sharing stopping working overnight. I didn't make any changes and a reboot didn't fix it. Trying to mount the shares would give "permission denied" messages on two different Linux clients. Windows file sharing worked fine.
In the end, I turned off the NFS service in the Web interface and turned it back on again, and this seems to have fixed it. Posted here for anyone else who experiences the same problem.