I agree that passing a razor on a sagging strop will ruin an already keen edge. It is simple geometry. If you have a taught strop it is very similar to a leather paddle strop. With the spine and edge of the blade held with uniform pressure against the leather surface the bevel should be essentially flat, in full contact with the leather. If catenary (the fifty cent word for sag) is introduced, the blade (regardless of pressure distribution) will then be describing a chord across the radius of the catenary. This will hold the bevel off the surface of the strop and force the edge to drag tangentially across the leather subsequently rolling and/or breaking the fine edge. You can do exactly the same thing with a taught strop or a paddle by lifting the spine of the razor while stropping.