Arborvitae can have selected branches "section out" while the remaining portions are fine. this can be caused by wind damage, cold damage, rodents, etc. I doubt this is being caused by insects such as spider mites. While all the same variety, their roots systems can differ, the soil they are growing in can differ even in a short distance. Close examination can reveal a broken trunk or rodent damage. You may see a canker that has girdled the branch in question. For a more local perspective, contact your local Extension Service in your county.