Large earthquakes can build mountains by uplifting bedrock, but they also erode them by triggering large volumes of coseismic landsliding. Using a zero-dimensional numerical model, we identify that the storage of sediment produced by earthquakes can affect surface uplift and exhumation rates across the mountain range. However, the storage also reduces the time span at which the impact of the earthquake can be measured, preventing the recognition of single earthquakes in many long-term records.