I think Sue is right, and your sandy soil is unable to retain moisture. Is this a beach area? You may be able to amend your soil with organic material, but if you're in an area with nothing but sand, it's probably going to just absorb the organic material without you having much to show for it. Apparently, Duranta species like rich organic soil that drains well. Your best bet may be to grow it in a container with an appropriate potting soil. Growing it in a container also means you may be able to shelter it if you get freezing weather.
If you aren't on the beach, you may want to start amending your soil to see how much it can be improved. Have a look at your neighbors' yards to see what their dirt looks like, and which plants they're growing. I'd think you could easily grow Gaillardia (Blanket Flower), and I wonder if you could also grow a heat-tolerant lavender such as 'Phenomenal'?
Plenty of other possibilities; I'd check with your local Native Plant Society or the Lady Bird Johnson Wildflower Center in Austin for suggestions about ornamental natives that will like your growing conditions.
Good luck,
Virginia
