As I understand it, having a class in natural resources, the majority of the city of New Orleans is built on top of marshland. Marshland will continue to sink over time due to decay of the plant material that it is mainly composed of. Even if they did build it up, it would immediately start compressing the marshland soil underneath and start sinking again. I don't think they would be able to keep it from sinking. Also I read where Houston is sinking faster than New Orleans ever thought about sinking.