Either way, that object in the 01.max scene you uploaded has broken vertices, i.e. each corner of that box consists of three separate vertices (that happen to be in the same position).
To fix this, you need to weld the vertices. You can do this in Edit Poly (Vertex sub-object mode > select all > Click 'Weld' option > select a really small threshold (e.g. 0.00001)) or you apply a Vertex Weld modifier with a very, very small threshold.
Edit: I just noticed that your geometry also has problems with surface orientations/normals. Try to select a face in your example scene and move it to the side - not all of the mesh will follow as expected! So you need to "flip" the faces that have this problem before you weld vertices.
Also note: your .max file has some serious problem - when opening it, I get the warning "14836 unused Animation Layer Control(s) removed".
Martin B
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