Batteryless or so called passive wearables are providing new and innovative methods for human activity recognition (HAR), especially in healthcare applications for older people. Passive sensors are low cost, lightweight, unobtrusive and desirably disposable; attractive attributes for healthcare applications in hospitals and nursing homes. Despite the compelling propositions for sensing applications, the data streams from these sensors are characterised by high sparsity---the time intervals between sensor readings are irregular while the number of readings per unit time are often limited. In this paper, we rigorously explore the problem of learning activity recognition models from temporally sparse data. We describe how to learn directly from sparse data using a deep learning paradigm in an end-to-end manner. We demonstrate significant classification performance improvements on real-world passive sensor datasets from older people over the state-of-the-art deep learning human activity recognition models. Further, we provide insights into the model's behaviour through complementary experiments on a benchmark dataset and visualisation of the learned activity feature spaces.