Here is a discussion on Mesh Refinement.

I didn't see that the issue was a failed mesh on one side. It was not that it didn't match the the right side, but that there was no mesh at all. If you reduce the maximum element size under Mesh Details, then do you get a successful mesh?

How was the geometry brought into the model for meshing?  Import a neutral file, through DesignModeler or through SpaceClaim?  

Check the geometry in DesignModeler with Tools --> Analysis Tools --> Fault Detection. Geometry should not have any errors before going to meshing.