Yes, could you please post the .3dm file of at least the object set in question?

Try this: 1) make sure that the little ring is a round circle and is also basically tangent, or relatively planar with the ends of the long curves.
2) go back to the number of profile rings you had on the main body, but add two extra long curves in the remaining quadrants to define those sides.

See my tutorial: http://moi3d.com/forum/index.php?webtag=MOI&msg=5188.1

It will teach you how to make the best of your Network shape. :-)

Mike