What are the mechanisms maintaining the Dune of Pilat?
As per @Richard suggestion, I think the best answer comes from dune-pyla.com. They provide a complete explanation of the evolution of the dune and a couple of great summary figures:


It seems that the material comes in large part from the Banc d'Arguin to the west through aeolian transport. The sand from the bank and adjacent areas is related to the material from the river Garonne to the north.



Part of the reason for the height is that they covered the preexisting Dune de La Grave with a pine forest during the XIX century to stabilize the sand and then the forest was covered by another additional 20-30 meters of sand. The dune is still migrating east at an average rate of around 7-8 m/year and burying the surrounding forest as it migrates.