Common problems with boxwoods include winter damage and root rot. These problems can cause boxwoods to suffer from brown or yellowing greenery, which damages the plant and causes it to look unattractive as well.
Exceptionally cold winters can cause damage to boxwoods, so if the leaves appear brown in the spring after the first thaw, don't be alarmed, just feed and water the plant as usual and it should recover. If fungal pathogens infect the root system of a boxwood shrub, it can cause serious damage if not treated quickly. Increase the amount of drainage around the plant and decrease the watering frequency to help the plant have a chance at recovering.