Social groups often exhibit a high degree of dynamism. Some groups thrive, while many others die over time. Modeling group stability dynamics and understanding whether/when a group will remain stable or shrink over time can be important in a number of social domains. In this paper, we study two different types of social networks as exemplar platforms for modeling and predicting group stability dynamics. We build models to predict if a group is going to remain stable or is likely to shrink over a period of time. We observe that both the level of member diversity and social activities are critical in maintaining the stability of groups. We also find that certain 'prolific' members play a more important role in maintaining the group stability. Our study shows that group stability can be predicted with high accuracy, and feature diversity is critical to prediction performance. Copyright is held by the International World Wide Web Conference Committee (IW3C2).