Recurrent neural networks (RNNs) are commonly applied to clinical time-series data with the goal of learning patient risk stratification models. Their effectiveness is due, in part, to their use of parameter sharing over time (i.e., cells are repeated hence the name recurrent). We hypothesize, however, that this trait also contributes to the increased difficulty such models have with learning relationships that change over time. Conditional shift, i.e., changes in the relationship between the input $X$ and the output $y$, arises when risk factors associated with the event of interest change over the course of a patient admission. While in theory, RNNs and gated RNNs (e.g., LSTMs) in particular should be capable of learning time-varying relationships, when training data are limited, such models often fail to accurately capture these dynamics. We illustrate the advantages and disadvantages of complete parameter sharing (RNNs) by comparing an LSTM with shared parameters to a sequential architecture with time-varying parameters on prediction tasks involving three clinically-relevant outcomes: acute respiratory failure (ARF), shock, and in-hospital mortality. In experiments using synthetic data, we demonstrate how parameter sharing in LSTMs leads to worse performance in the presence of conditional shift. To improve upon the dichotomy between complete parameter sharing and no parameter sharing, we propose a novel RNN formulation based on a mixture model in which we relax parameter sharing over time. The proposed method outperforms standard LSTMs and other state-of-the-art baselines across all tasks. In settings with limited data, relaxed parameter sharing can lead to improved patient risk stratification performance.