Looks like a variegated form of elephant bush, Portulacaria afra. It is not particularly delicate but will drop leaves readily if the watering is off. The soil looks a little heavy for succulents so that could be a contributing factor. And does that container have good drainage holes?

now that gal gave the latin name... check this out: https://duckduckgo.com/?q=Portulacaria+afra+propagation&t=ffcm&iax=videos&ia=videos

grow it in a pot like the succulent next to it ...

and after you propagate some pieces ... either throw out the old one.. or repot it in proper cactus mix .... in a pot with proper drain holes ...

ken

thanks! ok, I'll try propagating one stem and see how it goes.

it's in a glass vase. I had luck with just giving it a really carefully measured amount of water so it didn't get too wet -- that took it from almost dead to how it looks now. but I'll go ahead and replant with a proper pot & soil.

ILoveMod

Containers without drainage are not suitable for succulents. Those plants should be left to dry up between watering, and when watered - it should be thorough. Measuring amount of water is just an inconvenience, and not that good for the plant. Any succulent would have similar problems if overwatered, even jades. So the drainage is important, and that means well/fast draining potting mix, and the container with drainage hole(s). Most succulents also need very good light so they do not become etiolated. Try to propagate from stem cuttings - they grow easily, but only if the stem is healthy. Good luck, and maybe you can post photos of potted cuttings?