I've had that experience as well. I think the edges are too wet and the water seeps too deep and softens the edge, especially on single layer edges without any stiches. When I burnish on an edge that's too wet, it concaves on that edge.
I'll dampen the edge with a wrung out canvass, and mount it on a pony to help burnish with even pressure.
I'll try to attach a pic of the problem area and the stitched edge that I was happy with. Both just water and a nylon slicker on veg tan.