I just ran across this topic this morning, as I was having this same issue yesterday while drawing some building sections. I thought a hidden line in the plane of the section cut that was missing was causing the issue too. After playing with the model (unhiding the line) and trying, I found that the issue wasn't solved. After reading here, I went back and checked that no groups have textures.
Late last night, I came to the same conclusion as others have reached here. Include a third (for me) viewport to stack with my light and dark viewports for only 2d graphics. These would include faces to hide things beyond what I intend to show. Such as something touching the far end of a beam. Or things within a wall.
Question about stacking viewports though. If I stack my "2D Graphics" viewport on top, will its edge properties ovverride the properties of the cut edges of my main viewport? Or can you set a style with no edges, so that only faces are shown and the edge properties of a viewport below would be visible?