We investigate fixed points of affine mappings on a class of explicitly constructed probability simplices in a nonreflexive hybrid sequence space. The simplices are generated by a bounded coefficient profile whose minimum is attained at finitely many indices and is separated from all remaining values by a positive gap. A diagonal isometry transfers the problem to the space of absolutely summable sequences, where coordinatewise limits of approximate fixed point sequences can lose mass. We derive a coercive distance estimate that confines any lost mass to the finite set of minimum-weight coordinates. This estimate shows that a suitable orbit approaches a compact minimizing simplex and is therefore relatively compact. The closed convex hull of that orbit is compact and invariant, so a fixed point follows from Schauder's theorem. We also obtain a quantitative stability result that controls the distance to the minimizing simplex through the excess asymptotic radius. The proof does not assume that the ambient space has the fixed point property and keeps the conclusion restricted to the displayed finite-gap subsets.