I don’t know about MAX, but in Softimage, using the latest FBX import/export plugin (V7.1) doesn’t work (gotta love it when a new version breaks things). I typically use a version that’s two versions back (V6.1) and things seem to work fine - so - if you can, try testing some older versions of the FBX plugin.
There is another possibility, and that is you might have some transforms on those pieces - make sure to freeze your transforms on any model before exporting (as long as that doesn’t break animations, of course). I have a friend who gives me Blender models and they have a nasty tendency to snap to other positions, scales, orientations in the world when I hit “play”… I’m still trying to get him to remember to freeze transforms and remove any animations from non-animated objects.