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Current clinician-based and automated risk assessment methods treat the risk of suicide-related behaviors (SRBs) as static, while in actual clinical practice, SRB risk fluctuates over time. Here, we develop two closely related model classes, Event-GRU-ODE and Event-GRU-Discretized, that can predict the dynamic risk of events as a continuous trajectory across future time points, even without new observations, while updating these estimates as new data become available. Models were trained and validated for SRB prediction using a large electronic health record database. Both models demonstrated high discrimination (e.g., Event-GRU-ODE AUROC = 0.93, AUPRC = 0.10, relative risk = 13.4 at 95% specificity in a low-prevalence [0.15%] general cohort with a 1.5-year prediction window). This work provides an initial step toward developing novel suicide prevention strategies based on dynamic changes in risk.