I'm not completely sure I understand what you are trying to do, but here's a stab:
How did you originally chop off the bottom of the complex shape? From some playing with your model, it appears to me that the bottom edge may not be perfectly planar. If you reveal hidden lines, zoom in, and roam around, you find strange looking things like these:
[image: YkWv_ScreenShot2014-06-20at1.17.23PM.png]
[image: 8gqu_ScreenShot2014-06-20at1.18.11PM.png]
I think the intersect is generating Edges where bottom Edge segments of the shape lie in the plane, but leaving gaps where they do not, and as a result the intersections do not form closed shapes the way you expected.
HTH
Steve
PS: those sorts of tiny missing triangles are typical of what happens if you do many kinds of operations without first scaling up the model enough. SketchUp does not draw Edges when it thinks their Vertices are too close together, and that causes jagged edges and missing Faces.