Some wild rabbits are unable to be tamed. They exhibit the "tame mode" behavior, but when I try to feed them carrots they just go into breed mode.

Some users are reporting that this is also happening to wolves and ocelots (in snaphshot 14w32b at least), but whether or not that is confirmed is unknown to me.

After some more testing it seems like once you mess the taming process up and make a wild rabbit go into breed mode it cannot be tamed as giving it another carrot after it is willing still makes it go into breed mode.