I am convinced that it is in direct relation to how many epic buildings you have.
I just finished my 7th cheetah building a few days ago.
Prior to my 7th cheetah building I had.....
2 turtle
6 llama
6 cheetah
Under this configuration it took me 3 turtle pieces, 6 llama pieces and 10 cheetah pieces to get 1 token. This was the same before and after the Mayor's Contest update.
Upon completing my 7th cheetah building, Llama went from needing 6 pieces to 7 pieces. I need to pay closer attention to the other two to see how many pieces it takes. Llama just stuck out like a sore thumb because I was at getting one token per day and I missed it by 1 piece. I thought the pieces required was changing as I was adding new ones, but couldn't confirm it until now. I believe I started with Llama only needing 5.
I have read another thread where someone said they wrote EA about it and got a response back that said something to the affect of yes, the more you have, the more is required, but it will top out at some point and not go any higher. Although they did not tell him when it would top out and quit requiring more and more pieces. So for that, I have no answer either.