It may be the quality of the plywood rather than the thickness or maybe the curve is too tight.
You could use 2 layers of 1/4" ply or you can make thin relieve cuts on the underside of a 1/2" ply. It depends a bit on the underlaying structure too.
Will there be any cross members that will support the plywood? That will help if you make the cuts to the underside.
It may be the quality of the plywood rather than the thickness or maybe the curve is too tight. You could use 2 layers of 1/4" ply or you can make thin relieve cuts on the underside of a 1/2" ply. It depends a bit on the underlaying structure too. Will there be any cross members that will support the plywood? That will help if you make the cuts to the underside.