We investigate the behaviour of load-adaptive rerouting policies in the Wardrop model where decisions must be made on the basis of stale information. In this model, an infinite number of agents controls an infinitesimal amount of flow each, thus contributing to a network flow which induces latency. In our dynamic extension of this model, agents are activated in a concurrent and asynchronous fashion and may reroute their flow with the aim of reducing their sustained latency. It is a well-known problem that in settings where latency information is not always up to date such behaviour may lead to oscillation effects which seriously harm network performance. Two quantities determine the difficulty of avoiding oscillation: the steepness of the latency functions and the maximum possible age of the information T. In this work we ask for conditions that the rerouting policies must adhere to in order to converge to an equilibrium despite the information being stale. We consider simple po...