We combine Eulerian ice draft observations from moored ice‐profiling sonars with buoy‐ and satellite‐derived ice drift data to obtain Lagrangian observations of changes in the thickness distribution of sea ice circulating the Beaufort Sea. We examine repeat measurements of ice draft by identifying events where buoys or pseudobuoys made repeat overpasses within 30 km of ice‐profiling sonar‐equipped Beaufort Gyre Exploration Project moorings. Comparison of ice draft distributions from each overpass indicates that summertime melt rates are related to drift track, with more melt occurring in the southern Beaufort Sea than to the north. Additionally, we find that ice surviving summer in the Beaufort Sea since 2007 is similar in thickness to surrounding first‐year sea ice by the end of the following winter. These findings are supported by continuous ice thickness data from ice mass balance buoys. By examining “plumes” of pseudobuoys originating at each mooring location, we identify anomalous northward transport of ice in the southern Beaufort Sea in 2007 that likely contributed to the record‐breaking reduction in sea ice extent that year. We also find that repeat overpasses have been much rarer since 2007, due to reduced summertime sea ice extent in the Beaufort Gyre and possible changes in ice drift patterns. These changes contribute to diminished replenishment of multiyear sea ice volume in the Arctic.