Yellow or brown leaves on boxwood are caused either by a lack of nutrients or water.
Often, a lack of water becomes noticeable only after the dry period is long over. This happens in winter as well as in hot summer, because evergreen plants need water throughout. Only during the frost periods they must not be watered. Late damage (discoloration of the leaves) is then very protracted and can sometimes even result in the death of the plants.
Fertilizer against nutrient deficiency
If you have always watered sufficiently, it should be a nutrient deficiency. Then you can supply the boxwood with a slow-release fertilizer. Mature garden compost enriched with horn shavings or special boxwood fertilizer (available in stores) is suitable. It is also advantageous to mulch with compost, bark mulch and the like, which maintains soil moisture. However, it takes some time with the fresh green new shoots until the fertilization or soil improvement is clearly noticeable.
Roots can also be affected
In addition to the lack of water and nutrients, the roots of the plant could also be attacked. On the one hand by drought (see above), but more likely by waterlogging or by pests such as earthworms, rodents, beetles, etc.. In this case you have to dig up the plant and check the roots. If the roots are muddy and yellowish, it is a damage by waterlogging. Roots that have been eaten away indicate a pest.
By the way: boxwood tolerates pruning back into the old wood very well, it develops new shoots and becomes more compact. Severe pruning is also possible if boxwood becomes bare from the inside or suffers from late damage (see above).