There are several possible causes for yellowing and browning of boxwood. Winter injury usually shows up as more uniform browning on branch tips. Since in your case the problem is scattered throughout the hedge relatively randomly, it's more likely to be a fungal disease. One of the more common diseases of boxwood is volutella canker and blight. Plants are more susceptible to the disease if they have been stressed by winter injury or poor growing conditions. Unfortunately there is no effective fungicide control for this disease. Prune out and destroy affected areas and maintain plants in good health with adequate fertilizer and water.
Avoid overwatering, however, because excess soil moisture can lead to phytophthora root rot, which can cause large sections of the plant to turn brown. This soil borne fungus is also very difficult to eradicate. You may be able to suppress it by drenching the soil with a fungicide containing metalaxyl. Affected plants will have blackened, rotted roots.
Yet another possibility for the browning on your boxwoods is nematode infestation. Nematodes are microscopic worms that live in the soil and feed on plant roots. The plant is stunted and slowly dies. Symptoms are usually worst in hot weather, so this possibility seems less likely than one of the fungal diseases. No chemical control is available for nematodes in planted soil.