We analyze the stock market by modeling it as a timing game among arbitrageurs for beating the gun. We assume that (1) arbitrageurs are behavioral with a small probability, (2) the bubble soft-lands, and (3) the postcrash price increases as the X-day is postponed. Due to these assumptions, the effect of reputation assumes importance because any rational arbitrageur is willing to build a reputation in order to ride the bubble. It is demonstrated that the bubble persists for a long period as an outcome of a unique symmetric Nash equilibrium, even if all arbitrageurs are almost certainly rational.