Spring is a treacherous season to plant anything in the Sonoran Desert (other than succulents and palms). Fall is better, to give them time to adapt and settle in.

A lot of unrelated plants go under the name "jasmine." Do you still have the tag with the latin double name? Is it "Jasminum polyanthum"?

J. polyanthum is from southeast Asia. It needs uniformly moist well-drained soil, which sounds impossible but can be achieved in a pot with cactus soil, or in the ground in native desert soil.

Books will tell you it needs several hours of sun per day, BUT those are instructions for other climates. In the Sonoran desert, it will fry in the sun. So move it to a position with dappled shade, or against a north-facing wall, where it will have very bright indirect light.

About once a year, a lot of my stems die, even when new ones are sprouting. I don't know if this happens to anyone else, but it may be what is happening to yours, just a annual pattern. Let the dead stems become dry and brittle, and then they are easy to snap or snip and remove, leaving a better-looking plant. Sometimes I've just had to cut mine down very low and let it come up again to get it to look good.

Visit your nearest botanical garden, and ask them how they treat theirs.

It blooms once a year, in late winter, on new growth. They are inexpensive, so if this one fails, buy one in the fall and try again. It is a nice plant if you can keep it going. Best of luck with it!