The invisible ship problem is still around. I can't say what the root cause is. It seems to only affect the base designs and unmodified hulls (that is, where you don't artistically design the ship). I have noticed a few things recently:
1. Even if you do not check the 'Save as Template' box, the game will save all of your designs as templates.
2. Playing as the Iconians I used a small hull (Do the Iconians have the old Torian hulls?), and just threw some weapons on. Building them gave no problems. You could see them in the list, on the planet, and in space. I upgraded the design in the shipyard, and instantly it turned invisible. I went into the template list (where I believe both were visible), deleted the previous design, and upgraded all the existing ships. The result of this was that the ship reappeared in the shipyard, was blank on the planet view and in orbit, could be seen when launched, and was also invisible in the fleet and battle icons.

I still don't understand what's going on, but perhaps this will give someone a lead. I have also seen the Torians build huge defenders. I think that the hull may be scaled wrong. The small icon for the ship is also messed up, it looks low-res.