I had trouble with this for a long time, but I found the easiest way to farm them. Despite what people said, that isn't in the Sanctuary.
No, no. Go to Tatroi then leave past the area with the bunny and into the next zone as if you were going toward the ocean. You zone in under a large rock arch structure. In this area you'll always find at least two axe beak birds-- put Mearcle in and make sure she has her aviary skill 10/10. Kill those two birds, quickly zone out via the rock-arch exit and back in. Kill the two, rinse and repeat. I got the feathers quickly.
Now, I spent two hours at the sanctuary with little to show in terms of feathers... yeah, forget that. Maybe that area just doesn't like me.