Stable non-BPS states in F-theory

F-theory on K3 admits non-BPS states that are represented as string junctio ns extending between 7-branes. We classify the non-BPS states which are gua ranteed to be stable on account of charge conservation and the existence of a region of moduli space where the 7-branes supporting the junction can be isolated from the rest of the branes. We find three possibilities; the 7-b rane configurations carrying: (i) the D-1 algebra representing a D7-brane n ear an orientifold O7-plane, whose stable non-BPS state was identified befo re, (ii) the exotic affine E-1 algebra, whose stable non-BPS state seems to be genuinely non-perturbative, and, (iii) the affine E-2 algebra represent ing a D7-brane near a pair of O7-planes. As a byproduct of our work we cons truct explicitly all 7-brane configurations that can be isolated in a K3. T hese include non-collapsible configurations of affine type.