In this paper, we examine the problem of information storage on memristors affected by resistive drift noise under energy constraints. We introduce a novel, fundamental trade-off between the information lifetime of memristive states and the energy that must be expended to bring the device into a particular state. We then treat the storage problem as one of communication over a noisy, energy-constrained channel, and propose a joint source-channel coding (JSCC) approach to storing images in an analogue fashion. To design an encoding scheme for natural images and to model the memristive channel, we make use of data-driven techniques from the field of deep learning for communications, namely deep joint source-channel coding (DeepJSCC), employing a generative model of resistive drift as a computationally tractable differentiable channel model for end-to-end optimisation. We introduce a modified version of generalised divisive normalisation (GDN), a biologically inspired form of normalisation, that we call conditional GDN (cGDN), allowing for conditioning on continuous channel characteristics, including the initial resistive state and the delay between storage and reading. Our results show that the delay-conditioned network is able to learn an energy-aware coding scheme that achieves a higher and more balanced reconstruction quality across a range of storage delays.