Ice-shelf fractures frequently terminate where they encounter suture zones, regions of material heterogeneity that form between meteoric inflows in ice shelves. This heterogeneity can consist of marine ice, meteoric ice with modified rheological properties or the presence of fractures. Here, we use radar observations on the Larsen C Ice Shelf, Antarctica to investigate i) the termination of a 25 km-long rift in the Churchill Peninsula suture zone, which was found to contain ~60 m of accreted marine ice, and ii) the along-flow evolution of a suture zone originating at Cole Peninsula. We determine a steady-state field of basal melting/freezing rates and apply it to a flowline model to delineate the along-flow evolution of layers within the ice shelf. The thickening surface wedge of locally accumulated meteoric ice, which likely has limited lateral variation in its mechanical properties, accounts for ~60% of the total ice thickness near the calving front. Thus, we infer that the lower ~40% of the ice column and the material heterogeneities present there are responsible for resisting fracture propagation and thereby delaying tabular calving events, as demonstrated in the >40 year time series leading up to the 2004/05 calving event for Larsen C. This likely represents a highly sensitive aspect of ice-shelf stability, as changes in the oceanic forcing may lead to the loss of this heterogeneity.