Web search queries without hyperlink clicks are often referred to as abandoned queries. Understanding the reasons for abandonment is crucial for search engines in evaluating their performance. Abandonment can be categorized as good or bad depending on whether user information needs are satisfied by result page content. Previous research has sought to understand abandonment rationales via user surveys, or has developed models to predict those rationales using behavioral patterns. However, these models ignore important contextual factors such as the relationship between the abandoned query and prior abandonment instances. We propose more advanced methods for modeling and predicting abandonment rationales using contextual information from user search sessions by analyzing search engine logs, and discover dependencies between abandoned queries and user behaviors. We leverage these dependency signals to build a sequential classifier using a structured learning framework designed to handle such signals. Our experimental results show that our approach is 22% more accurate than the state-of-the-art abandonment-rationale classifier. Going beyond prediction, we leverage the prediction results to significantly improve relevance using instances of predicted good and bad abandonment