Once a tree dies it is difficult to determine why. In general arborvitae do not have a lot of insect and disease issues. Some reasons for decline may be planting too deeply, drought, poor soil drainage, possible insects, etc. See our publication on these types of problems http://extension.umd.edu/sites/default/files/_images/programs/hgic/Publications/HG86%20Common%20Abio...
There is a new insect pest called the Japanese cedar longhorned beetle that can cause branch dieback and browning in certain host plants. Damage appears as dead branches in sizes as small as a pencil to main trunks. Before pruning dead plant material, look along the branches and trunk for small insect holes. All you can do is prune and dispose of infected branches.http://extension.umd.edu/hgic/invasives/japanese-cedar-longhorned-beetle
At this point all you can do is prune dead plant material and remove dead plants. Keep the plants well watered during dry periods and make sure mulch is no thicker than several inches and away from the trunks. Monitor the health of the trees and send us photos as soon as you notice symptoms.