Student Dropout Prediction (SDP) is pivotal in mitigating withdrawals in Massive Open Online Courses. Previous studies generally modeled the SDP problem as a binary classification task, providing a single prediction outcome. Accordingly, some attempts introduce survival analysis methods to achieve continuous and consistent predictions over time. However, the volatility and sparsity of data always weaken the models' performance. Prevailing solutions rely heavily on data pre-processing independent of predictive models, which are labor-intensive and may contaminate authentic data. This paper proposes a Survival Analysis based Volatility and Sparsity Modeling Network (SAVSNet) to address these issues in an end-to-end deep learning framework. Specifically, SAVSNet smooths the volatile time series by convolution network while preserving the original data information using Long-Short Term Memory Network (LSTM). Furthermore, we propose a Time-Missing-Aware LSTM unit to mitigate the impact of data sparsity by integrating informative missingness patterns into the model. A survival analysis loss function is adopted for parameter estimation, and the model outputs monotonically decreasing survival probabilities. In the experiments, we compare the proposed method with state-of-the-art methods in two real-world MOOC datasets, and the experiment results show the effectiveness of our proposed model.