with Maya it's usually either the material or something getting disconnected / bent out of shape in the history and causing the link between a shape node and material to get borked. Sacrificing your first-born (or deleting history every third operation) generally helps to avoid this sort of bullshit.
Turn on the Poly Count HUD and select the object to see if it still holds any vertices. If the second column says 0 you're out of luck. You can also turn on shape nodes in the outliner to check if there's anything below the transform node. Have you been switching between different versions of Maya? I've had this happen…
Did these objects already get combined/extracted previously? There's a few cases where blank shape nodes are left over. Maybe try saving as .ma format, and search for the model names in a text editor, check their data.