The problem has been resolved. Here's everything I did and extra data in case it helps you:
Extra Data:
I could no longer see the device on the Network Devices listing in Windows 7 Explorer even though I could still ping the device and could access the interface via IE(/Chrome).
EVERY TIME I access the device through the IE interface, it said it had two (shared) folders (one for each drive), but Navigator2 still could not see the two folders -- yes, I refreshed and restarted the program often.
Steps I took in getting the drives back -- I don't know which one was the solution key:
I ran a Disk Check on both drives. No extreme error messages but still didn't see any access.
I renamed one of the shared folders. I did NOT delete and recreate the Shared folder. (A future test?)
I renamed the shared folder listing back to the original name.
Brought the device to my main desk from the storage location where it usually operates. In addition to having it plugged into my local switch I also plugged in the USB connection to my main PC.
... Oddly, the direct USB connection didn't register on my main PC.
Frustrated, I shut down both the device (I had done this multiple times) as well as the main PC I had it plugged into, said screw it and went to bed. Basically I shut down the whole thing.
... I also sacrificed a young goat to the gods before going to bed if you think that might have been a factor. The Gods seem to LOVE capretto.
Restarted the drive and after it came up, restarted the PC -- The drive enclosure was still on the switch as well as connected via USB cable to the main PC.
The status, according to Windows and accessing via IE was unchanged.
FINALLY: Even though it was still not visible, I decided to run a direct "Map Drive" sequence through Windows Explorer. That is, I Mapped the Folder as I would any existing, visible folder.
IT WORKED! In addition to working, the network listings now show the device as well.
The next step will be to return it to the storage site and see if the access remains active.
I have removed the USB link and it is still active.
Things I did NOT do!!!:
I did not delete and remake the Shared Folder.
I did not remove and re-seat the drive! In the past this has cause the system to (unexpectedly) reformat the drive.
I hope this information is helpful. I honestly can't see anything other than the sacrifice that had any direct influence.
I think the Check Drive actions might have corrected the situation and next time I'll try mapping the drives after each step.