Not an easy one to answer. Look at your past 5-10 rounds. Have you been improving? You will receive different opinions regarding this but overall you need to consistently improve on your game.
No one has discovered the magic formula or number yet but devs have confirmed it is a round vs downs.
Just play well, constantly get to a higher round than the last game with fewer downs. You will eventually get the knife. It took me 6 months to get the knife. Patience is the key.
Thanks for posting!
As maxslick noted, Indeed, Zombies ranks are dynamic, and will change within normal operation. Please feel free to check out our article at Activision Support.
Wish you the best in your Zombie endeavors!