Illustrator :: Object Layering Opacity - Fill Doesn't Block Out Object Paths Beneath

I am having some trouble with a file in Illustrator CS6. Within a layer, when I add a fill to an object, the fill doesn't block out the object paths beneath. For instance, say I have a square object overlapping a circle object in Layer 1. The square object is above the circle in the layer. When I add a fill to the square, the circle stroke still shows through the square even though the overlapped part should be blocked out by the fill. The square is set to normal visibility, and I have made sure that there are no duplicate paths that would account for what I am seeing. (I.e., it's not a case where there's a second identical circle path that is on top of the square, so that it remains visible in spite of the fill.)
 
Other details:
- I'm mainly working with a white fill, but the problem is the same with fills of any color
- When there's a fill color in the circle path as well, the circle's fill color *is* blocked out—just not its stroke.
- I have restarted Illustrator and restarted my computer and these have not changed anything.
- There are other layers within the same document where the normal layering rules work.
- I tried copy/pasting some of the problem objects into a new document, and in the new document, the fill works properly.
- If I move the problem objects to another layer, then the fill works as it should. But as I'm dealing with a number of paths, it doesn't make sense to create a layer for each to solve the problem.
 
I can't tell if it's a matter of working in too large or complex a file.