I think the normals of your faces look into the wrong direction. I see this often in MAX models. Maybe Max does render such faces still without problems but most of the other applications respect the alignment of the normals more accurate and thus render them inwards-out.

But maybe your material in Max is checked as "double sided" then you also will not see this problem visually in Max but will see it in-game since Direct-X does not render them double-sided without any special materials / shaders.