Not all layers converted because of empty or unsupported content

Unless you are actually animating vector paths or using shape animators like Trim Paths, or using the C4D rendering engine to extrude a shape layer, there is absolutely no reason to convert vector layers to shape layers. 

If you do need to do any of those things the Illustrator file must be prepared using a specific set of standards that include:

• No Gradients
• No Raster Effects like blurs, drop shadows
• No Brushes on paths
• No textures on filled shapes
• No 3D effects

If you do not follow these guidelines you will end up with a solid gray object in the converted layer, a bunch of groups that are hard to manage, or a failure. The vector engines are different and you must follow the rules if you are to be successful.

One more point. When creating vector artwork for use in video production, you should have Snap to Pixel turned on and Pixel Preview in Illustrator. Thin horizontal and vertical lines should be at least 2 pixels (points) thick. You should make sure that all the horizontal and vertical edges of your vector artwork line up with the pixel grid and shapes, especially rectangular shapes, should always be an even number of pixels high and wide to make it easier to precisely position them using whole pixel values on the pixel grid in After Effects to prevent edges from degrading and changing color when they are antialiased and turned into pixels.

Yes, the problem is in the AI file and how stuff is created there. Without a screenshot of the layer panel to understand the grouping and compound paths as well as any potential appearance effects applied nobody can tel lyou much, though. The devil is in the details.

Mylenium