This study examined the relationships between achievement goals, motivation instability, and learning persistence in asynchronous distance classes by focusing on mastery goals and performance-avoidance goals. A longitudinal online survey was conducted among university students in Japan at two time points. The first survey had 171 respondents. Out of them, 91 responded to the second survey. The data of the 91 students were analyzed. The results of partial correlation analysis indicated that mastery goals were negatively related to motivation instability and lack of persistence, while performance-avoidance goals were positively related to lack of persistence and unrelated to motivation instability. Mediation analysis indicated that the negative indirect effect of mastery goals on lack of persistence via motivation instability was found, and that the direct effect of mastery goals on lack of persistence was not found. The results highlight the vital role that mastery goals play in learning during asynchronous distance classes.