The rapidly retreating Thwaites and Pine Island glaciers together dominate present-day ice loss from the West Antarctic Ice Sheet and are implicated in runaway deglaciation scenarios. Knowledge of whether these glaciers were substantially smaller in the mid-Holocene and subsequently recovered to their present extents is important for assessing whether current ice recession is irreversible. Here we reconstruct relative sea-level change from radiocarbon-dated raised beaches at sites immediately seawards of these glaciers, allowing us to examine the response of the earth to loading and unloading of ice in the Amundsen Sea region. We find that relative sea level fell steadily over the past 5.5 kyr without rate changes that would characterize large-scale ice re-expansion. Moreover, current bedrock uplift rates are an order of magnitude greater than the rate of long-term relative sea-level fall, suggesting a change in regional crustal unloading and implying that the present deglaciation may be unprecedented in the past ~5.5 kyr. While we cannot preclude minor grounding-line fluctuations, our data are explained most easily by early Holocene deglaciation followed by relatively stable ice positions until recent times and imply that Thwaites and Pine Island glaciers have not been substantially smaller than present during the past 5.5 kyr.