User engagement in search refers to the frequency for users (re-)using the search engine to accomplish their tasks. Among factors that affected users’ visit frequency, relevance of search results is believed to play a pivotal role. While multiple work in the past has demonstrated the correlation between search success and user engagement based on longitudinal analysis, we examine this problem from a different perspective in this work. Specifically, we carefully designed a large-scale controlled experiment on users of a large commercial Web search engine, in which users were separated into control and treatment groups, where users in treatment group were presented with search results which are deliberate degraded in relevance. We studied users’ responses to the relevance degradation through tracking several behavioral metrics (such as query per user, click per session) over an extended period of time both during and following the experiment. By quantifying the relationship between user engagement and search relevance, we observe significant differences between user’s short-term search behavior and long-term engagement change. By leveraging some of the key findings from the experiment, we developed a machine learning model to predict the long term impact of relevance degradation on user engagement. Overall, our model achieves over 67% of accuracy in predicting user engagement drop. Besides, our model is also capable of predicting engagement change for low-frequency users with very few user signals. We believe that insights from this study can be leveraged by search engine companies to detect and intervene search relevance degradation and to prevent long term user engagement drop.