Carolina Jessamine is an evergreen to semi evergreen meaning that in your climate it will often lose most or all of the foliage in mid to late winter depending on the particular site where it is growing. The plant is not really prone to any particular disease problems. I suspect that the spots on the foliage are caused by a fungal leaf spot. You could spray a fungicide such as Daconil prior to the appearance of the spots each year to prevent them. However I question whether or not the spray is necessary as fungal spots often occur on older foliage that is about to drop anyway.
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