OK, my curiosity got the best of me. Here are the numbers:
Players
round1: 2507
round2: 2057 -> 82% of round1
round3: 1687 -> 82% of round2
round4: 1398 -> 83% of round3
round5: 1147 -> 82% of round4
round6: 932 -> 81% of round5
round7: 776 -> 83% of round6
round8: 642 -> 82,73% of round7
round9: 543 -> 84,58% of round8
round10: 450 -> 82.87% of round9
round11: 385 -> 85.56% of round10
round12: 325 -> 84.42% of round11
Very interesting to me that the amount advancing per round is actually increasing. I suspect that there is something about skill differentials that allows more players to be knocked out early in the tournament, and as players' skill levels converge, we get closer to that theoretical elimination rate of 12.5%.
I do not believe that players joining different amounts of games per round is a factor. The reason is that if everybody played until they won, then 50% of players would join a game 2. 25% would join a game 3 and 12.5% would be eliminated. The same result as if everyone joined all 3 games. And, I suspect, the same amount no matter what permutations you do of players playing more or fewer games. (Except, of course, the permutation that has people not joining games even though they do not have a win).
Edited the posts above, but credit due to the original posters of these stats:
knubbel for rounds 1 through 7 and
general roy for rounds 8 and 9.