I'm sorry to hear that some of your arborvitae trees are dying. They look like beautiful specimens in your picture. It could be a disease issue, insects or an a-biotic issue such as water logged soil, root obstruction or string trimmer damage.
If possible, I would like for you to take some samples from the tree that is starting to show symptoms. These samples should include branches that have both living/healthy material and dead/dying material. I will send these to the U.K. Plant Disease Diagnostic Lab in Lexington and they will be looking specifically at the transition zone between healthy and diseased tissue. You can deliver the samples in a garbage bag to the Jessamine County Extension Office at 95 Park Dr. in Nicholasville. Our office is currently closed to the public but we can receive samples on our front porch. Please include your name and phone number with the sample.
I would also like for you to take some more pictures of the dead and dying trees. Specifically, I would like to see some up-close shots taken of the ground level and the newly impacted leaves and branches.
You are welcome to call me at (859) 885-4811 or email me at email@example.com if you have more questions.