I have had this issue occur at least 3 times during my testing.  When I move to the "next" ship by either hitting the space bar for the current ship or clicking on the button to move to the next object, the view will move to an area that does not appear to have a ship in it.  However, I know that I had a ship in that location.  If I right-click on a nearby cell, the ship will appear and remain visible as it moves to the target cell, but disappear again once it arrives.  I had an Explorer ship that had 32 moves and I was able to make it appear and disappear as I made it move 2 or 3 cells at a time.  After this "invisible ship" bug occurs, within a few turns the program hard crashes.  When I restart the game and load the most recent save, the problem is gone and the game functions as expected.  This has always happened when I am well into the game (this one is 412 turns in and I have 38 core worlds, 117 colonies, and 108 ships).

So, to summarize, it appears that ships becoming invisible is a symptom indicating that a hard crash is about to occur.

Here is a screen snapshot of the properties window of the executable: