In large-scale distributed systems data aggregation is a fundamental task that provides a global synopsis over a distributed set of data values. Epidemic protocols are based on a randomised communication paradigm inspired by biological systems and have been proposed to provide decentralised, scalable and fault-tolerant solutions to the data aggregation problem. However, in epidemic aggregation, nodes failure and churn have a detrimental effect on the accuracy of the local estimates of the global aggregation target. In this paper, a novel approach, the Robust Epidemic Aggregation Protocol (REAP), is proposed to provide robustness in the presence of churn by detecting three distinct phases in the aggregation process. An analysis of the impact of each phase over the estimation accuracy is provided. In particular, a novel mechanism is introduced to improve the phase that is most critical for the protocol accuracy. REAP is validated by means of simulations and is shown to achieve convergence with a good level of accuracy for a reasonable range of node churn rates.