Deep learning algorithms are known to experience destructive interference when instances violate the assumption of being independent and identically distributed (i.i.d). This violation, however, is ubiquitous in clinical settings where data are streamed temporally and from a multitude of physiological sensors. To overcome this obstacle, we propose CLOPS, a replay-based continual learning strategy. In three continual learning scenarios based on three publically-available datasets, we show that CLOPS can outperform the state-of-the-art methods, GEM and MIR. Moreover, we propose end-to-end trainable parameters, which we term task-instance parameters, that can be used to quantify task difficulty and similarity. This quantification yields insights into both network interpretability and clinical applications, where task difficulty is poorly quantified.