Is it still sinking?
Here in Houston, parts of the city were sinking do to pumping of ground water. Since that practice was stopped, the ground stopped sinking. I assumed this is the same reason why New Orleans has sunk.
Along the Gulf coast we actually have many active faults. Those faults are usually caused by Salt Domes, or wedges of land slowly sliding into the Gulf. The rate of slid is so slow that the land is replaced by sediments.