The most common issue for a Rosemary dying is a watering issue; too much or too little.
Botrytis blight fungal infection rots the older leaves in the center of a rosemary plant. It flourishes in high relative humidity, poor air circulation, and cloudy weather conditions. Watch for yellowish brown, irregular leaf spots or water-soaked spots on plant stems. During humid weather, the fungus produces a fuzzy brown to gray growth on the surfaces of injured plant parts or dead plant material. When disturbed, the fungus emits a cloud of spores.
Remove and destroy infected plants and debris to control spread of the disease. Prune overgrown plants, and increase spacing between container plants to improve air circulation. Avoid mulching the plant beds with organic materials, because these harbor fungal spores. Instead, use crushed stone, pea gravel, or rocks, which dry out quickly and reflect warm sun onto the plants and reduce humidity still further.