Basil grows best in warm weather. It is not frost tolerant. The most likely cause of black leaves on basil plants, especially in cooler months, is frost damage. To prevent frost damage, protect plants with a windbreak. Do not remove damaged leaves from plants until after the danger of frost has passed, because the black leaves help protect lower leaves from being damaged by frost.
When basil leaves begin to dry out, they may turn brown or black. Although basil should not be given too much water, too little water can cause them to desiccate and wither. Leaves damaged by lack of water will probably not recover, and should be removed from plants.
Fungal infections can cause leaves to turn black. There are many types of fungal infections that could affect basil, but the most likely culprit is Fusarium oxysporum f. sp. basilicum. This infection, which is known as fusarium wilt, causes leaves to darken and drop from the plants. This pathogen is soil borne, and it can live in the soil for as long as 12 years. There is no treatment available for this infection, and it is advisable to avoid growing basil and mint in the area for 12 years to prevent the disease from being redistributed in the area. Instead, move basil to other areas of your property, or consider growing it in containers.
There is one main insecticide that has been approved for treatment of insect infestations on basil, and that is Javelin. This treatment is only effective for killing various types of caterpillars. It will not work on other pests that may infest basil. If this insecticide is ineffective, try using beneficial insects, hand picking, or insecticidal soaps. You may also try alternative treatments, such as reflective mulches or traps.