Certified GKH Gardening Expert
No, they are naturally droopy. Do not stake them up. They need to be droopy in order to "learn" to be rigid and hold the plant structure up under its own weight. Let them droop without staking and prune at the correct times.
This article will help: https://www.gardeningknowhow.com/ornamental/flowers/duranta/care-of-duranta-plants.htm