Why can't I use loop cuts after beveling? I'm creating a simple length of wood and have used bevel to round the edges a little. Every face still has 4 vertices but for some reason, I can only use loop cut on the new faces and not around the whole thing.

Anyone have any idea why? 
Thanks for any help.
I tried that with Blender 2.81 and a beveled cube. It works. So it seems that the bevel is not the reason for the problem.
Check the geometry: Go into edit mode an "Merge Vertice by distance" (v2.80) or "Merge" (CTRL-V in edit mode). Ensure that the normals of the faces are pointing outside. If this does not help there is a workaround: In edit mode select all edges in question and subdivide instead of loop cut.