With self-driving vehicles (SDVs), pedestrians cannot rely on communication with the driver anymore. Industry experts and policymakers are proposing an external Human-Machine Interface (eHMI) communicating the automated status. We investigated whether additionally communicating SDVs' intent to give right of way further improves pedestrians' street crossing. To evaluate the stability of these eHMI effects, we conducted a three-session video study with N=34 pedestrians where we assessed subjective evaluations and crossing onset times. This is the first work capturing long-term effects of eHMIs. Our findings add credibility to prior studies by showing that eHMI effects last (acceptance, user experience) or even increase (crossing onset, perceived safety, trust, learnability, reliance) with time. We found that pedestrians benefit from an eHMI communicating SDVs' status, and that additionally communicating SDVs' intent adds further value. We conclude that SDVs should be equipped with an eHMI communicating both status and intent.