Vehicle automation is a potentially highly advantageous concept in terms of reducing traffic accidents, e.g., due to distractions by non-driving related tasks (NDRTs) or decreased vigilance. The driver needs to have a thorough understanding of the vehicle automation system and a moderate level of trust in it for the advantages to be realized. System failures inherently adversely affect trust, however, a completely reliable system is unrealistic. In the present study, we explore how drivers' trust in vehicle automation affects their NDRT engagement, vigilance, and initiative takeover performance after experiencing a system failure. In the induction experiment, seventyseven participants were divided into three groups by their level of trust (distrust, appropriate trust, excessive trust) in the highly automated vehicle. All experienced five "hazardous events" in the formal experiment, the second of which was a system failure. Relevant results indicated that the system failure affected drivers differently depending on their levels of trust. Drivers' NDRT engagement decreased after the system failure due to a decline in trust but increased during subsequent driving as trust recovered. Vigilance was higher in drivers who were distrustful, but the post-failure decrease in vigilance was higher compared to others. Drivers who were distrustful were more likely to initiatively take over the vehicle as evidenced by higher resulting acceleration upon encountering the hazards. The maximum resulting acceleration decreased with the sequence of hazardous events but increased with the level of risks. The findings of this work may be useful in terms of trust calibration processes, technological improvements to vehicle automation systems, and the promotion of automated vehicle usage.