Ligustrums can suffer from certain diseases that cause the symptoms that you have. Most of the diseases that cause this type of problem are related to the plant roots. As Ligustrum plants age, they become less able to withstand stress, and root stress can happen during times of drought as well as during times of abundant rainfall. About the only remedy is to make sure that your plants are kept moist but never wet for extended periods and never allowed to dry out. During both of these types of moisture extremes, roots can die, which leads to plants becoming more susceptible to disease organisms. You can try to prune them slightly to encourage new growth and fertilizing them.

Thanks for your inquiry.

Happy Gardening!
The PlantMaster