The stratigraphic record is an important archive of how Earth systems have responded to different rates and magnitudes of climate change. Much of what we know about past climate comes from paleo-environmental proxies preserved within sedimentary deposits, but proxy records of the same event often show significant differences, leading to uncertainty in climate reconstructions. Recent work has underscored the concept that intrinsic variability in sedimentation extends over large spatiotemporal scales in many sedimentary environments. Here we use a stochastic sedimentation model with a known input signal to evaluate whether variable sedimentation may contribute to discrepancies between proxy records. We find that even small variability in sedimentation results in uneven preservation of time, leading to significant differences between proxy records. Some records fail to preserve any evidence of the input signal, and others preserve signals with different apparent magnitudes, durations, and shapes. Our results suggest that averaging across multiple low-resolution records may be a robust approach to accurately reconstructing paleoclimate and paleo-environmental conditions, particularly in depositional settings where variability in sedimentation is large relative to long-term sedimentation rates.