In the domain of machine learning, Neural Memory Networks (NMNs) have recently achieved impressive results in a variety of application areas including visual question answering, trajectory prediction, object tracking, and language modelling. However, we observe that the attention based knowledge retrieval mechanisms used in current NMNs restricts them from achieving their full potential as the attention process retrieves information based on a set of static connection weights. This is suboptimal in a setting where there are vast differences among samples in the data domain; such as anomaly detection where there is no consistent criteria for what constitutes an anomaly. In this paper, we propose a plastic neural memory access mechanism which exploits both static and dynamic connection weights in the memory read, write and output generation procedures. We demonstrate the effectiveness and flexibility of the proposed memory model in three challenging anomaly detection tasks in the medical domain: abnormal EEG identification, MRI tumour type classification and schizophrenia risk detection in children. In all settings, the proposed approach outperforms the current state-of-the-art. Furthermore, we perform an in-depth analysis demonstrating the utility of neural plasticity for the knowledge retrieval process and provide evidence on how the proposed memory model generates sparse yet informative memory outputs.