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Fault tolerance in MPI becomes a main issue in the HPC community. Several approaches are envisioned from user or programmer controlled fault tolerance to fully automatic fault detection and handling. For this last approach, several protocols have been proposed in the literature. In a recent paper, we have demonstrated that uncoordinated checkpointing tolerates higher fault frequency than coordinated checkpointing.Moreover causal message logging protocols have been proved the most efficient message logging technique. These protocols consist in piggybacking non deterministic events to computation message. Several protocols have been proposed in the literature. Their merits are usually evaluated from four metrics: a) piggybacking computation cost, b) piggyback size, c) applications performance and d) fault recovery performance. In this paper, we investigate the benefit of using a stable storage for logging message events in causal message logging protocols. To evaluate the advantage of this technique we implemented three protocols: 1) a classical causal message protocol proposed in Manetho, 2) a state of the art protocol known as LogOn, 3) a light computation cost protocol called Vcausal. We demonstrate a major impact of this stable storage for the three protocols, on the four criteria for micro benchmarks as well as for the NAS benchmark.