Winter jasmine is one of the deciduous jasmines. Each fall, it drops its leaves and goes dormant. If your winter jasmine appears dead, don't dig it out and replace it. Wait until the following March. Its yellow flowers will appear if it's still alive. New leaves will unfurl shortly after blooming.
Jasmine is not drought tolerant and requires a moderate amount of water each week. If it's been dry in your area for a few weeks and your jasmine looks withered or the leaves are falling off, water your plant well for the next several days. If it hasn't been too stressed, the plant will perk up. If it doesn't perk up, it may be dead. Cut the plant back to about 3 feet tall, keep it watered for the rest of the growing season and it may produce new growth the following year.
Jasmines need morning and evening sun or dappled afternoon sunlight. If your winter jasmine is exposed to full sun during the hottest time of the day, your jasmine suffers sun stress. The leaves burn and the plant can die. If your winter jasmine's leaves turn brown and dry in a sunny location, shade it with a sheet or transplant it to a shadier location.
Although winter jasmine has few pest problems, it is subject to spider mite infestations. Spider mites feed on the plant juices and can kill a plant. The spider mites appear as tiny, white spots in a mesh of fine webbing. If the jasmine appears to be dying from spider mites, cut it to the ground and destroy the infected vines. When new growth appears, providing a balanced fertilizer encourages healthy growth.