Yaupon hedge

Question

Part of yaupon hedge puts out, then leaves turn brown and fall off.

Answer 1

You may have pest, disease or even water and nutrient issues; difficult to say from just your description.
Inspect the leaves and bark for more signs of the problem.
This article will refresh on the care needed.
https://www.gardeningknowhow.com/ornamental/shrubs/holly/growing-yaupon-holly.htm