Hello,
first of all thanks for answering.
Here is how I configured my DNS 320L to setup a Time Machine volume for Mavericks:
1. I created a new share under Account Management > Network Shares with read and write permissions for all users; the share have both CIFS and NFS protocols enabled because it's not possible to select/deselect them (the check boxes are gray and not editable);
2. Under Applications > Local Backups I selected Time Machine on the left, I enabled it selecting the check box and then I created a new Time Machine share selecting the share created at point 1.
On my Mac I opened Time Machine preferences, clicked "Select Disk... " and I selected the share created on the NAS;
Time Machine worked fine for same days using this share then it failed with the message I reported when I opened the thread.