  We report pressure-dependent neutron diffraction and muon spin
relaxation/rotation measurements combined with first-principles calculations to
investigate the structural, magnetic, and electronic properties of
BaFe$_2$S$_3$ under pressure. The experimental results reveal a gradual
enhancement of the stripe-type ordering temperature with increasing pressure up
to 2.6 GPa and no observable change in the size of the ordered moment. The ab
initio calculations suggest that the magnetism is highly sensitive to the Fe-S
bond lengths and angles, clarifying discrepancies with previously published
results. In contrast to our experimental observations, the calculations predict
a monotonic reduction of the ordered moment with pressure. We suggest that the
robustness of the stripe-type antiferromagnetism is due to strong electron
correlations not fully considered in the calculations.
