In this paper, we revisit the common claim that double auctions necessarily generate competitive equilibria. We begin by observing that competitive equilibrium has some counterintuitive implications: specifically, it predicts that monotone shifts in the value distribution can leave prices unchanged. Using experiments, we then test whether these implications are borne out by the data. We find that in double auctions with stationary value distributions, the resulting prices can be far from competitive equilibria. However, we also show that double auctions display strong equilibrating tendencies once traders can leave without replacement as time progresses. Taken together, these findings suggest that the exit of traders over time is a key driver of equilibrium prices in double auctions.