I type this as a public service announcement to others – so you do not have to spend 3 hours on Apple technical support for something that should take 10 minutes.
If your Finder stops seeing the network devices, it is probably a simple issue – the firewall. And yes .. before you say it … I should have thought of that way earlier into the process instead of blindly following the Apple level 1, then level 2, then level 3 technical support who never thought to try such an incredibly obvious element.
In my case, all of our devices are using McAfee All Access. Somehow (either by a router firmware upgrade or a McAfee upgrade), the firewall swapped the network from home/work to public, thereby blocking the local network.
Under preferences of the McAfee All Access console – simply change it back – under Type (right side).
Hopefully that saves someone else 3 hours.