It appears to be very localized to that certain part of the plant. Is there some type of external condition that could be causing this (like a large dog urinating on the plant) or a sprinkler spraying right into it? The rest of the plant appears to be fairly healthy with signs of new growth. You may want to take a clipping and go see a local garden center you trust.

the stems looks pale white.. rather than brown..

google : Euonymous scale ...

and tell us if that is what it is... and whether it is spreading to the other parts ...

i am not a big fan of these.. for this reason.. i would destroy the plant and move on with life.. finding something else for the spot ..

ken

Thanks. I have 6 of these in a row so I don't want to plant something else in it's place....as it would look rather strange. The others are doing fine. Yes, it could be a dog. It seems like every dog in the neighborhood uses my yard since we don't have a dog. All of them want to mark my yard. Really wish people would be responsible for their animals.

Looks like scale to me. Check the stalks and see if they have scaley whitelike bugs. Compare the dead ones to the live ones.

If scale go to your garden shop and purchase some oil spray. Spray it really good, several times. Follow instructions. This will kill the scale.

I had this problem and now the one that was bad is completely healed and shaped up nicely.