Analysis of ICESat-1 data (2003-2008) shows significant surface lowering of Totten Glacier, the glacier discharging the largest volume of ice in East Antarctica, and less change on nearby Moscow University Glacier. After accounting for firn compaction anomalies, the thinning appears to coincide with fast-flowing ice indicating a dynamical origin. Here, to elucidate these observations, we apply high-resolution ice-ocean modelling. Totten Ice Shelf is simulated to have higher, more variable basal melting rates. We link this variability to the volume of cold water, originating in polynyas upon sea ice formation, reaching the sub-ice-shelf cavity. Hence, we propose that the observed increased thinning of Totten Glacier is due to enhanced basal melting caused by a decrease in cold polynya water reaching its cavity. We support this hypothesis with passive microwave data of polynya extent variability. Considering the widespread changes in sea ice conditions, this mechanism could be contributing extensively to ice-shelf instability.