Illustrator :: Why Does One Of Levels Disappear

I've created a design with four elements:northwest, northeast, southeast, and southwest; each is on a separate level.   I created the NW object first, the copied and rotated 180 deg to create the NE object and recolored.  I then copied the NW and the NE objects and rotated them 180 deg to create the SE and SW objects.   See below.
 
Now I'd like to add a background below all of them, but when I do, the NW object disappears.  See below.
  
I note that the little meatball next to the disappearing level is filled in, but it's empty for the other three levels.  But I don't know what the two different meatball types mean.  Each layer has a group layer and 26 sublayers.  Some of the sublayers have different screen modes, and there is also a drop layer effect on one.  They look identical to me, but with so many layers I might have missed something. 
 
I'm using AI CS6 on a Dell computer.