Yellow and thinning carolina jasmine leaves by: Steve
I would suggest you test the soil for nutrient deficiency. If nitrogen is low, older leaves (which are the located on the first foot or two of the plant), can turn yellow and fall off. Some may die and remain hanging on to plant.
Inspect the underside of the leaves for insects to rule out that as a problem. Because your the other Carolina jasmine vines are doing OK it sounds like the problem can be isolated to that specific jasmine plant.