I think they should make it where the longer you've been in, the easier it is to throw you out. That way, if you just come in, you've got a lot more stamina than Ultimo Dragon, who's been in for ten minutes. That way, if Ultimo Dragon, who's on a roll and has eliminated several people, tries to throw you out as soon as you get in, he can't. I like the idea of the button tapping for eliminations because it prevents things like that from happening.
Because that happens to me A LOT.
How about this: the longer you're in, the less stamina you have. But to maintain the possibility of making through the entire rumble, every time you eliminate someone you gain some stamina. That way, if you get on a roll, you can't get accidentally eliminated because someone is fresher.