A decade-long population study of 1,776 adults across eight rural Ugandan villages found HIV-related stigma declined substantially from 2014-2024, but became increasingly concentrated within a persistent minority group. Public stigma toward people with HIV showed trait-like stability (intraclass correlation 0.35), with individuals maintaining their relative stigma rankings over time, while perceived stigma—beliefs about others' attitudes—converged to universally low levels regardless of baseline views. Notably, traditional demographic markers failed to identify the stigma-persistent group, with socioeconomic and cultural factors explaining less than 3% of variation. This concentration pattern suggests that while population-wide anti-stigma interventions succeeded broadly, a core subset remains resistant to attitude change. The findings challenge conventional targeting strategies that rely on demographic profiling to identify stigma carriers. For HIV elimination efforts, this implies that residual stigma may be particularly entrenched and require novel intervention approaches beyond education campaigns. However, as this is a preprint study from a single rural region awaiting peer review, the generalizability to urban or different cultural contexts remains uncertain, and the specific mechanisms driving stigma persistence require further investigation.