I'm trying to print a model of a wireframe Echidnahedron, which is a very spiky geometric shape. However, the versions posted in My Models after uploading are missing some parts. This is especially strange because the parts which are missing seem to depend on the overall scale of the model.
Compare these three versions, which should all look the same except for the thickness of the bars, but don't:
Your model looks like it consists of 150 open ended shells. Shapeways automated software (Mesh Medic) must have got confused as to what should be joined where so decided some bits could be left out Basically, all of your shells need to be closed (watertight) and even then if there's matched geometry between two or more shells the software still might leave stuff out.
If you haven't already, grab yourself a free copy of NetFabb Studio Basic. Its good for checking and repairing your models. Also NetFabb's Cloud Service will boolean your model shells together in the same way that Mesh Medic does (as well as performing other checks & repairs). Both are invaluable tools when building models for 3D printing.