As discussed in this thread, objects exported in Lightwave (OBJ/MTL) format often have an incorrect illumination model set. (For instance, in four successive exports of an object, with slight modifications made between exports, only one one occasion was one instance of a material correctly exported as 'illum 2'. The object contains 7 materials that should have been exported as 'illum 2' each time; instead, they typically exported as 'illum 1'.)
Procedure to test:
The material's Ns value is correctly exported. However, if the exported object is imported back into SH3D, all materials render as matte -- that is, without shininess. On subsequent exports, the material's Ns value is reset to 0.0 0.0 0.0.
Workaround: Edit MTL file and change the illum value for all non-translucent materials where Ns > 1.0 to 'illum 2.'
Translucent materials also tend to be exported as 'illum 1' rather than 'illum 4'; however, this is less obvious a failure on re-import [presumably] because SH3D takes its cue as to the proper illuminational model for translucent materials from the material's 'd' and 'Ni' values.