Adverse event detection is critical for many real-world applications including timely identification of product defects, disasters, and major socio-political incidents. In the health context, adverse drug events account for countless hospitalizations and deaths annually. Since users often begin their information seeking and reporting with online searches, examination of search query logs has emerged as an important detection channel. However, search context - including query intent and heterogeneity in user behaviors - is extremely important for extracting information from search queries, and yet the challenge of measuring and analyzing these aspects has precluded their use in prior studies. We propose DeepSAVE, a novel deep learning framework for detecting adverse events based on user search query logs. DeepSAVE uses an enriched variational autoencoder encompassing a novel query embedding and user modeling module that work in concert to address the context challenge associated with search-based detection of adverse events. Evaluation results on three large real-world event datasets show that DeepSAVE outperforms existing detection methods as well as comparison deep learning auto encoders. Ablation analysis reveals that each component of DeepSAVE significantly contributes to its overall performance. Collectively, the results demonstrate the viability of the proposed architecture for detecting adverse events from search query logs.