I've had shotguns since the first few weeks of the game's release. I've de-ranked to the knife twice since then. The first time was on Tranzit while trying to mess around and uncover perma perks and other secrets. Quit out on rd 1-5 several times and I was de-ranked the next day. I continued playing as usual and was promoted rather quickly.
The second time was on the day that Die Rise came out. I played a few games of Turned, so the downs in that mode combined with dying in every stupid way imaginable on Die Rise, and I was a skull with a knife the next day. I got my stuff together and my buddy and I went for a run to 46 on the same map. Still didn't rank up. Later played with another friend who isn't very good and carried her to 40 and quit out with zero downs. The next day, I was back to skull with shottys and haven't looked back.
Some observations: Kill/Down or Kill/Death ratio does seem to play a big factor. Playing on normal is probably the largest factor as I have plenty of skulls on my friends list with a higher KD than myself. I watch their games and they only play custom games on easy.. Also, I think that co-op games are required in order to achieve the highest rank. You CANNOT achieve the shotgun emblem while only playing on solo as far as I've seen. You can play several games on solo, then play 2-3 good co-op games and you should be able to rank up assuming your KD is there, AND you consistently make it to at least rd 15.
Lastly, I believe it is NOT overall KD ratio. It is a running average based on your last x amount of games. That is why you can rank down if you just quit out on rd 1 too many times.
My current K/Down ratio is a bit over 170 and over 200 in co-op games. Roughly 67K kills and 385 downs overall. My high rds are 25 with 0 downs on Tranzit(players quit), 28 and 0 downs on Bus Depot(buddy lagged out), 45 on Town, 46 on Die Rise, and 36 on Buried(have been to 43 and 38, but lagged out both times)