It appears you have backface culling on so you are not seeing the faces where the normals are facing away from you. Try toggling back face culling and see if that fixes your problem.
Also, since maya 2009 or so it's not uncommon for faces to lose their shader connection. In that case just select the object and reassign the shader.
update:
actually looking at this a second time I think option two is more likely.
"If I have seen further it is by standing on the shoulders of giants." Sir Isaac Newton, 1675