Features lost when extruding polygons between two TINs

I am trying to transform a collection of adjacent simple polygons to a collection of simple polyhedrons. My approach is to create two constant-elevation rasters representing the upper and lower boundaries of the polyhedrons, convert these two rasters to TINs, and then use the Extrude Between tool to generate the polyhedrons. However, I find that some of the features are lost (see gaps in the figure) and there appears to be some weirdness going on in the edge definitions of the resulting polyhedrons.

If I am not doing something wrong, is there an alternative approach to vertically extruding polygons to create polyhedrons?