I was able to correct this SA-NS410 connection issue after several weeks of frustation. Using the NS Setup App on my iPhone, I could setup and generate the test tone provided by the app, but when I would try to connect using iTunes from my Mac, or from the Music app on my iPhone, the SA-NS410 would not be available in the AirPlay selection list.
A blog post by Poppa Gadget on the SA-NS410 helped me solve the problem. Here's what he had to say:
"It turns out that despite the User Guide mentioning a WEP security key clearly in the "Setting Up for a Wireless Network" section, WEP is not supported. Simply changing my network to use WPA-PSK has fixed the problem and the speaker is now working as it should."
I have an Airport Extreme wireless router - so I opened the excellent Airport Utility (Go -> Utilities -> Airport Utility), double-clicked on my Airport Extreme, clicked the Edit button, selected the Wireless tab and determined that my Wireless Security was set to WPA2. Apparently that's not supported either. By changing the Wireless Security to WPA/WPA2 Personal, the SA-NS410 sprang to life and is working perfectly.
Wireless Security settings may be the root problem for others who have experienced this frustrating behavior with their SA-NS410. I really like the product's performance - but the finicky setup leaves much to be desired.
Hope this helps!