From what I've read in this forum, I think that they definitely would raise the red flag if you kept on winning. You have to remember their one and only goal is to take your money - never to give you theirs.
Constant winnings without a single loss? I think the casino would ask you to leave pretty fast, or start employing distractions to try and throw your game off. They don't just want you to stop winning, they want to get back everything they lost and come out ahead at the end of play.
JackBlack, sure it could raise a read flag with the casino if you win a lot or have a good streak going. However, if you are being fair and sticking to the rules, there's not much they could do. However, i have heard of casino banning people who constantly win.
The main intention of a casino and gambling in general is for the house to win more than the player(s). Again, you also have to remember that the house has the right to deny entry to anyone they are not comfortable with.
A consistent winning streak is one thing and a big win is very much another. IMO, it would depend on how much you were winning.
I guess this would depend on the scale or amount of the winnings. No casino wants to be on the losing end since it is business and profit is the driving factor. If you're winning good amounts, then the casino would probably think that you are cheating the system.
Makes you really sick to think that if you had a really good winning streak that they would ask you to leave. Looks like to me that if that happened to someone, they would be in the press trying to bad mouth that casino just to stop people from spending their money there. That being said, I don't know anyone who has had that long of a winning streak.