The DNS-320 uses the AFP (Apple File Transfer Protocol) to connect to OS X. In the latest Mavericks relaease Apple has dropped all support for AFP devices. They are now using their own proprietary system called SMB2. I am having a lot of problems with mine as well and have yet to find any solution to make it work properly again. I know this is no help but I wanted to post to give you a little more understanding. If I find any solutions I will follow up.
I had the same problem with a D-link DNS-320.
The following worked for me (Manual back up):
Set Time Machine backups off to allow manual back-up.
Create one alias of your NAS share in the desktop. (I don’t know why, I first had to create the share alias in a external USB drive and then move the alias to the desktop cause mavericks didn’t allow me to create the alias directly in the desktop.)
After using the “back up now” option in the time machine menu, just wait for a couple of seconds and double click your time machine share alias. This will mount the share and time machine back up starts immediately.
It seems as if double click initialize the communication and then the back up works normally.
I hope this helps.