Acute Kidney Injury (AKI) progression from KDIGO Stage 1 to Stage ≥2 in the ICU is associated with increased mortality, need for renal replacement therapy, and prolonged stay. Most existing predictive models are limited in handling heterogeneous multivariate temporal data, and real-time interpretability, hindering real-time clinical decision-making. We present a framework for \emph{continuous} prediction of AKI progression that employs temporal abstraction, Time-Interval-Related Pattern (TIRP) mining, and the Fully Continuous Prediction Model (FCPM) to deliver continuously interpretable risk estimates. Using state temporal abstraction, raw multivariate clinical temporal data are transformed into Symbolic Time Intervals (STIs) series from which frequent TIRPs ending with the AKI progression event are mined. FCPM learns a model that consists of the mined patterns, which then estimates in real-time their completion probability as new clinical data arrives, leveraging the time-duration distributions when the pattern is unfolding. We further introduce Prolonged Temporal Discretization (PTD), a supervised temporal state abstraction method that chooses cutoffs whose STI time durations are longer in the pre-event data compared to admissions data without the event. A rigorous evaluation on a cohort of 1,343 ICU patients shows that FCPM combined with PTD achieves an AUC-ROC of 0.838 and a mean lead time of 5.8 hours, significantly outperforming LSTM, ResNet, TFT, and XGBoost baselines in both discrimination and earliness.