I am actually, partially in the same boat as you. I noticed a similar behavior, occurring whenever I would download v1.2.009 beta from their servers. For whatever reasoning, everything is fine in v1.11 but once I upgrade, there are 13 ships which essentially become invisible whenever I go to a shipyard to view their models.
Strangely, at least for me, I've noticed this effects the ship designs for: Combat Transport, Cruiser, Destroyer, Dreadnought, Excalibur, Fire Hawk, Missle Boat, Paladin, Phoenix, Ranger, Sledge Hammer, Sniper, Thunder, Star Avenger, and Star Dragon models.
It also seems to only happen, in regards to all the different race designs, except for Humans. If I select having Human styled ships, all those ships (and the others) appear as normal, but if I change to either Altarian, Torian, Drengin, or Yor styled, those above 13 ships become missing, once I go into the shipyard.
I also contaced Support about it, since I hadn't seen any thing like it mentioned here on the forums, but I only sent my request about a day and half ago. I figure since no one else seems to be having this problem, it's probably something on my end, yet I've uninstalled and reinstalled the game many times already, trying to figure out what it is.
The one thing which I later found (after I sent my support e-mail) was that the ships still produce just fine, if I try and build them. It simply seems to be effecting me, when I go into the shipyard to view/modify those particular core ships.
Anyways, as you can see, at least there is one other person who has a similar problem as you had....well, at least your initial problem. I'm not getting flooded by the automated response messages.