Yes, I have a fairly extensive network already set up. And yes, network discovery is enabled.
Perhaps I should have also mentioned a couple of things: 
I am a network engineer by profession so not exactly a newbie when it comes to winding my way around a simple home network.
computers, printers, wireless devices, media servers all included, there are well over 2 dozen devices currently on the network and all of then, except the DNS320 show up in the network neighborhood. 
I can not find a setting in the device to enable this function but given the type of device it is, it's inconceivable to me that it would not be discoverable. 
And as I mentioned, I can access the device and map shares using the IP. I haven't tried by name because it has always been simpler and lees error ****e to use IPs. But now that you mention it. I give it a try. Though that really has nothing to do with this issue.