Ok, I repeated my test from a couple nights ago, so I'll share it here. Just remember, you asked for it.
I have a new kitchen knife I received for Christmas from my wife. I marked a 3" section of the blade so it would at least have that as similar to the test knives in the rest of the thread. I sharpened it on a 220 grit Norton water stone, followed by 1000 grit King and then the medium 204 (Sharpmaker) rods at a back bevel of 17, and final microbevel of 20 degrees per side. The edge would whittle hair off the medium stones.
I made 300 cuts into the poly cutting board I wanted to use, as I don't have any lumber around for a cutting board. I did this just to see what would happen to the edge. These were rocking cut, chef's style slices, as though dicing up a bell pepper. After these cuts, the edge would still whittle a beard hair. This knife has been used and at this point I found a small chip/dent in the edge in the area used for testing. I wasn't going to sharpen it out at this point, so off to the cutting board.
I began cutting 3/8" hemp rope from Lowe's, in sets of 20. Each time I alternated the direction of the slice, heel to tip for 20, tip to heel for 20. I tested all the way up to 400 cuts, testing for paper slicing after each 100 cuts. After 400, it would still slice paper cleanly on the first try. There was some snagging at the damaged area, and the chip/dent appeared to be a bit larger, but the rest of the edge cut paper no problem.
So tonight I removed the chip, resharpened the edge on just the 1000 King stone and 204. Then I repeated the rope cutting portion of the test. After 425 cuts, I still got clean slices in paper, both with and across the grain of the paper (top to bottom/side to side). Here is where my results differ pretty greatly. This knife is part of a set that cost $50. I'm guessing the steel is something like 5Cr13MoV or 440A or something, I don't know and it's not marked. I'm going to leave the edge as it is and continue, just to see how far it goes.