I purchased 3 Desmodiums at the BSF Convention in Orlando 5 years ago on the recommendation of a good friend of mine who lives in Deland- zone 9b, I live in southern Palm Beach County-zone 10. So far no problems at all except for slight yellowing of some leaves. I have switched to a time released 360 day 18-5-8 fertilizer and a suppliment fertilizer called MicroMax. The MicroMax is rather expensive, $110 for 50 lbs. Between the two new fertilizers the new leaves are dark green and it seems like they are producing more volume of flowers. Desmodium air layers easily in about a month, also roots easily from cuttings under mist, 8 seconds every 10 minutes. I over potted them into 15 gallon squat pots using Pro Mix with mycrrohazae, also rather expensive- the old saying is that you don't put a $5 plant in a 5 cent hole! The only drawback is that I like to walk barefoot thru the garden and nursery, Desmodium has thorns that put Brazilian Rain Trees to shame, some get 4" long when in full growth mode. One that got dropped on the ground and forgot to pickup went thru the bottom of my Sperry Topsiders Boat shoes! I haven't tried it yet but I am told that they grow readily from root cuttings. The flowers don't last long but they come out in mass with more purple than green leaves. They also grow readily from their seed.
BTW the MicroMax has also cured the yellowing on my Wrightii religiosa vietnanensis! I tried Ironite, drill press shavings, watered with steel wool rusty water to no avail.