A sediment particle traversing the fluvial system may spend the majority of the total transit time at rest, stored in various sedimentary deposits. Floodplains are among the most important of these deposits, with the potential to store large amounts of sediment for long periods of time. The virtual velocity of a sediment grain depends strongly on the amount of time spent in storage, but little is known about sediment storage times. Measurements of floodplain vegetation age have suggested that storage times are exponentially distributed, a case that arises when all the sediment on a floodplain is equally vulnerable to erosion in a given interval. This assumption has been incorporated into sediment routing models, despite some evidence that younger sediment is more likely to be eroded from floodplains than older sediment. We investigate the relationship between sediment age and erosion, which we term the “erosion hazard,” with a model of a meandering river that constructs its floodplain by lateral accretion. We find that the erosion hazard decreases with sediment age, leading to a storage time distribution that is not exponential. We propose an alternate model that requires that channel motion is approximately diffusive and results in a heavy tailed distribution of storage time. The model applies to timescales over which the direction of channel motion is uncorrelated. We speculate that the lower end of this range of time is set by the meander cutoff timescale and the upper end is set by processes that limit the width of the meander belt.