i don't have a7, but i remember a similar problem i once had in a6 (all frames there, no anim).
a) do you have multiple groups, like one closed mesh for the leg, one for the head etc? make them just one.
b) maybe the fbx exporter doesn't read your skinning/envelope modifier correctly. maybe you have to restrict the influence of bones to certain vertices by assigning them to the appropriate bones, not by just enveloping the mesh (c4d needed that step).