Drawing 3D shapes in 2D

I want to display an arbitrary slice of a 3D polygonalized object.

To this end, I have tried making the distance between the near and far faces of the frustum very small -this method almost works. The problem is that often some parts of the object (that should be displayed) are omitted in seemingly random fashion with each redraw.

This doesn’t happen with my 3D views (and the only difference between my 3D and 2D views is the frustum length).

What could be causing this problem?

What is a better way of displaying a 2D (very thin) slice?