The pinching-antenna system (PASS) has been proposed as a promising solution for mitigating line-of-sight (LoS) blockages by dynamically repositioning pinching antennas (PAs) along a dielectric waveguide. This paper develops a fairness-oriented downlink design for a non-orthogonal multiple access (NOMA)-enabled PASS, where the longitudinal placement of PAs and the NOMA power allocation coefficients are jointly optimized to maximize the minimum user signal-to-interference-plus-noise ratio (SINR) across all users under transmit power and waveguide constraints. A soft-blockage channel model incorporating waveguide attenuation and imperfect channel state information (CSI) is developed. To ensure the feasibility of successive interference cancellation under CSI uncertainty, a conservative SINR evaluation framework is proposed. The resulting non-convex max-min SINR optimization problem is efficiently solved using a tailored particle swarm optimization (PSO) algorithm. Numerical results demonstrate that the proposed design improves the minimum user SINR by approximately 7-10 dB compared with fixed-antenna systems and non-robust optimization baselines under moderate blockage and imperfect CSI.