This paper investigates the stability of departure time choice within a population of commuters that need to pass through a bottleneck of constant capacity. It is shown that the corresponding utility function is monotonic if and only if the marginal utility rate at the destination is a non-increasing function of time. This result unveils some fundamental difference in the dynamics of the morning and evening commutes and explains the many instances of non-converging behaviors reported in the morning commute literature. It also broadens their scope insofar as it is not restricted to a specific type of adjustment mechanism or schedule preferences. Yet, this paper also recognizes the important explanatory power of the equilibrium assumption and investigates under which circumstances the dynamic process can still be approximated by its equilibrium. The analysis of various simulations sheds light on the influence of specific behavioral parameters and on some systematic biases related to the equilibrium approximation.