STEM education, which means integrated thinking, attracts the attention of early childhood educators and researchers. Engineering education, which naturally serves STEM integration, contributes to children's problem-solving skills with failure analysis and continual improvement habits of mind. Children need adult support in this process due to their developmental characteristics. This study focuses on the roles of teachers in situations where children fail to solve the problems they encounter in the engineering design process. In this direction, the research was carried out with a case study. The participants were 17 preschool teachers working in southwestern Turkey and 255 children in their classes. The data for the study were collected through observation and a semi-structured interview protocol. The data were analyzed by content analysis. According to the results, teachers facilitated failure analysis and continual improvement processes in the problems faced by children by encouraging them to rethink the problem, encouraging them to persist, and inviting communication and cooperation with friends. The findings highlight teacher encouragement as important in children's failure analysis and continual improvement processes.