UPDATE: 2014-02-09 / Sunday / 11:30 AM EST / -5UTC
In the secondary test site, I started stripping the menus present down to the very basics, the thinking was to scale down to a simple menu with only the top level pages, which are at 6 pages.
Of the 5 menus that were present, first I started renaming them ...
Menu - Desktop One
Menu - Desktop Two
Menu - Mobile
Menu - One
Menu - Leftover From Another Theme (whose name we shall not mention here, because we are in love with this theme!! LOL)
We see where in the SQL DB the menus show up in the wp_terms section of the DB.
In the course of this diagnosis, we are nosing around in the PHPMyAdmin and in the functions of the SQL Database, because we have been forced to take some interest in how this stuff works.
Ok, so we go into the database overall and we perform the 'analyze' ... we 'repair' ... and overall we find that the database is not reporting any error messages to best of our ability to discern these things.
I will add that we are dogged, determined, and so we go into a mental comparison mode, if it does this here, then xxx, and so on. This kind of thinking paid off when we delved into the menus, all five of them, looking for anomalies, to see which ones worked, which did not, and what were the differences between each of them.
AHA!!!!!!!!!!!!!!!! We found an anomaly. In Menu - Basic, carrying only the six top level pages, the place marker for the page 'contact' had no link to the actual page, it was essentially 'empty' ... how this occurred I do not know.
To test my theory, I deleted the last main nav entry of 'contact' with the empty linkage. I re-added the current 'contact' page ensuring there was linkage, ... would the menu function save this menu addition/page to the menu this time, where in the past, it WOULD NOT save the addition to the menu??? It did save the amended/added page to the menu. Well, hot damn.
THIS WAS THE BIG BURP, THE HUGE HICCUP. Something so simple, this was like a beaver dam in the data flow. Damn. Crud. Crikey.
Thanks all :)