It seems that Mathematica will save 3D plots with shading that is not supported.
It does say in the errors that it does not (yet) support it, so I guess you already know about this issue.
Errors produced are:
ERROR: A PostScript error occurred.
ERROR: Type: Feature not (yet) implemented: Shading type 4
ERROR: Operand stack (max top 10 items):
ERROR: Execution failed due to a PostScript error in the input file.
It refused to let me upload the file as it was larger than 256k, sorry (it's around 2Mb).
An example of the lines that I suspect to be causing the problem is:
<</ShadingType 4/ColorSpace[/DeviceRGB]/DataSource[0 190.395 95.686 0.312 0.318 0.914 0 187.401 98.496 0.312 0.264 0.871 0 189.886 97.698 0.426 0.68 1 ]>>shfill