Subnano cluster catalysts, while highly promising due to unique activity, selectivity, and atom-efficiency, are limited in wider applications, as they are prone to deactivation via sintering. Even size-selection, which was previously shown to reduce sintering of nanoparticles, cannot reduce the sintering of highly fluxional subnano clusters due to their inherent isomeric diversity. Here, we use a combination of theory and experiment to show that Pt clusters on Al2O3 exhibit size-dependent sintering resistance. We furthermore show that Pt4/Al2O3 and Pt7/Al2O3 are "magic" sinter-resistant cluster sizes. Their stability is attributed to the greater degree of bulk-like crystallinity of the dominant isomers. In addition, we identify different spatial signatures characteristic of the sintering of clusters with differing sintering stabilities.