In this case the fix is to rotate the object a few degrees - enough to move the vertices off the sectioning plane. 


1. Rotate the object slightly (in this case 3º) about an axis parallel to the cutting plane (Z axis for a vertical section); this moved the segment endpoints out of the cutting plane, allowing the cross section calculation to succeed.
2. Note that this didn't help with the existing "Model-to-Sheet" views - Regenerating the views didn't update the orientation.