I noticed that a small section of my hedge seemed to die fairly quickly. I think the affected area is all stemming from
one branch
Unfortunately your photo was not attached and you don't mention the type or age of the hedge. Are you talking about a single plant in a row of plants or part of one plant. If it is a single plant, I would be looking under the surface for the problem either drainage or the roots. If only part of the plant is affected I would be looking for signs of insect activity, maybe borer.