The problem with increasing the maximum bet when you've just lost half your bankroll that you're making it easier for someone to win the other half as well. While it seems like the obvious thing to do is to leave things as they are and hope that the big player comes back and loses it all, that's easier said than done when he's just taken half your coins from you. Your natural reaction is to protect yourself by reducing the maximum he can win at once.

To keep your risk of ruin sensibly low, you need to reduce your maximum bet as you lose, and only increase it when you win.