Bacterial blight?

Could be a root rotting fungus one one kind or another. Some species of root rotters are very specific as to what they kill and what they don't. Usually when I hear that one branch at a time dies I think of verticilliums. I know that Japanese maples are very susceptible to verticilliums but I don't know about any of these plants you have. Daphnes are usually very susceptible to root rots though.

Burrowing rodents are another possibility, if they bore tunnels through the clerodendron's roots but leave everything else alone ...

Thanks for the suggestions - I am going for the verticillium theory - whatever it is, I think that location isn't going to have a Clerodendron any more. How ironic - here I thought I would have such a battle with suckers, and instead I can't keep one alive.

Your state Cooperative Extension office may be able to help with diagnosis. If the soil in that spot is infested with verticillium you would want to know, as there is a wide host range.

At this point there are other things growing in that area that do not appear to be suffering, that can grow on to fill the space, but if I ever plant something else there I will check a list.