The mesh is not watertight (manifold)
Cell fracture is having some problem with your mesh because it cannot easily recognize an enclosed volume to work with. As you can see in the image sequence below there are some vertices that, despite looking apparently connected, they are not.
The meshes created by converting an extruded curve are currently made this way.
The solution in this specific case would be to run thr Remove doubles command form the Vertices sub-menu (Crtl+V while in edit mode with all the vertices selected).
Here's a comparison between reults after and before merging the overlapping vertices: