Pinching-antenna systems (PASS) enable near-field beam focusing using radiating points along a dielectric waveguide, but coherent spherical-wave superposition makes their channels sensitive to small user displacements. This sensitivity is critical for power-domain non-orthogonal multiple access (NOMA), where successive interference cancellation (SIC) requires the weak-user layer to remain decodable at the strong user. We develop spatially robust PASS-NOMA designs that optimize antenna placement and power splitting over bounded service areas (SAs), with a preset decoding order and explicit SIC-feasibility constraints. We propose a worst-case design for quasi-static users and an ergodic design for codewords spanning representative SA positions, and characterize their achievable rate regions. Numerical results show that, despite SIC requiring weak-user decoding in both SAs, NOMA outperforms orthogonal multiple access (OMA) with a shared placement under both robustness models except when the strong user is served at low rate. In the ergodic regime, this advantage can persist even against OMA with per-user antenna reconfiguration.

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