Q.My holly bush is dying
Certain branches are dying from the outermost leaves down the branch to where it’s connected to the main stem. Other branches around it are not affected. I’ve trimmed it several times in the last year, removing the affected areas. However, it continues to happen. Should I remove the Holly or is there something I can do to restore my plant to good health? I’ve only had the plant about two years. The other Holly I bought at the same time is doing well.

From the image it appears to be leaf scorch, but you could also be dealing with a fungus issue.
Prune away the damaged plant material and dispose of.
I would use a broad spectrum fungicide on the plants.
Make sure the soil is well draining and pull any mulch back at least 6 inches from around the trunk of your plants.
You can mulch with some good compost to add nutrients and aide in soil compaction and drainage.