Ask Mr. Smarty Plants

The first thing we do, when asked questions about a specific plant and problems with it, is to determine where that plant is native and whether being planted in the wrong soils and climate might be the cause of the problem. Follow this plant link to our webpage on Gelsemium sempervirens (Carolina jessamine). By doing so and using the link under "Additional Resources" we found on the USDA Plant Profile Map that Carolina jessamine grows natively no nearer to Nevada than Texas, and far east Texas, at that. That means that Las Vegas NV, in Clark County at the southeast tip of Nevada, is well out of the native range for this plant.

However, if you have the plant and most of it has been growing well for 3 years, we next need to see if there is a problem in the location of the plants with the yellow leaves. On that same plant webpage, you will see these Growing Conditions:

"Growing Conditions

Water Use: Medium
Light Requirement: Sun , Part Shade
Soil Moisture: Moist
Soil pH: Acidic (pH<6.8) , Circumneutral (pH 6.8-7.2)
Cold Tolerant: yes
Heat Tolerant: yes
Soil Description: Moist, well-drained, humus-rich soil. pH adaptable. Sandy, Sandy Loam, Medium Loam, Clay Loam, Clay.
Conditions Comments: The best flowering occurs in full sun."

So, what does this tell us about the differing leaf colors? Well, not much. It does well in both sun (6 or more hours of sun a day) or part shade (2 to 6 hours of sun a day) and blooms better in full sun. But this concerns leaf colors, not blooms. Although it likes acidic soils, which you probably don't have, it is pH adaptable. That leaves us with the soils, which no doubt are the same soils in both parts of your garden. Look at the Soil Description above. What our radar is picking up is the phrase "Moist, well-drained..." A plant with yellowing leaves is usually suffering from chlorosis, caused by a problem preventing the roots from accessing necessary nutrients from the soil. We found a previous answer from Las Vegas that is very apropos to your problem, although it concerns a different plant. From that previous answer:

"Yellowish leaves could indicate chlorosis, or lack of iron being taken up by the plant from the soil. This is often caused  by poor drainage and/or dense clay soil, which causes water to stand on the roots. Again, this could  be a problem caused by planting, perhaps without any organic material added to hole, or damage to the tiny rootlets that take up water and trace elements, including iron, from the soil."

Now we feel the problem is narrowed down to that particular area, and it is up to you to do the rest of the detective work, as we don't make house calls. Check to see if the soil is too moist, or the plant is on a grade where excess water drains into the plant roots. If you have automatic watering, consider redirecting some of it, or simply cutting down on the water. You could try adding some iron supplement to the soil in that particular area, but not too much. Native plants in general don't much care for fertilizer. That plant's roots may simply be drowning, and adjustment in its environment is the best fix and the cheapest. And we don't recommend adding nitrogen. While nitrogen does encourage the production of more green leaves and is usually applied to grasses, the addition of nitrogen will just enourage more leaves to grow, probably still yellowing, and thus reduce the energy available for blooms.