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With the growing adoption of deep learning models in different real-world domains, including computational biology, it is often necessary to understand which data features are essential for the model's decision. Despite extensive recent efforts to define different feature importance metrics for deep learning models, we identified that inherent stochasticity in the design and training of deep learning models makes commonly used feature importance scores unstable. This results in varied explanations or selections of different features across different runs of the model. We demonstrate how the signal strength of features and correlation among features directly contribute to this instability. To address this instability, we explore the ensembling of feature importance scores of models across different epochs and find that this simple approach can substantially address this issue. For example, we consider knockoff inference as they allow feature selection with statistical guarantees. We discover considerable variability in selected features in different epochs of deep learning training, and the best selection of features doesn't necessarily occur at the lowest validation loss, the conventional approach to determine the best model. As such, we present a framework to combine the feature importance of trained models across different hyperparameter settings and epochs, and instead of selecting features from one best model, we perform an ensemble of feature importance scores from numerous good models. Across the range of experiments in simulated and various real-world datasets, we demonstrate that the proposed framework consistently improves the power of feature selection.