We combine measurements of ice velocity from Landsat feature tracking and satellite radar interferometry, and ice thickness from existing compilations to document 41 years of mass flux from the Amundsen Sea Embayment (ASE) of West Antarctica. The total ice discharge has increased by 77% since 1973. Half of the increase occurred between 2003 and 2009. Grounding-line ice speeds of Pine Island Glacier stabilized between 2009 and 2013, following a decade of rapid acceleration, but that acceleration reached far inland and occurred at a rate faster than predicted by advective processes. Flow speeds across Thwaites Glacier increased rapidly after 2006, following a decade of near-stability, leading to a 33% increase in flux between 2006 and 2013. Haynes, Smith, Pope, and Kohler Glaciers all accelerated during the entire study period. The sustained increase in ice discharge is a possible indicator of the development of a marine ice sheet instability in this part of Antarctica.