We investigate a non-Hermitian extension of the Su--Schrieffer--Heeger model that incorporates spin-dependent SU(2) gauge fields, represented by non-Abelian couplings between lattice sites, as well as independent nonreciprocal hopping amplitudes. This framework gives rise to a rich phase structure characterized by complex-energy braiding and tunable non-Hermitian skin effects. By employing the generalized Brillouin zone approach, we analyze the bulk-boundary correspondence and identify topological transitions protected by chiral symmetry. Notably, we demonstrate that non-Abelian gauge fields significantly enhance the dynamical resilience of the system, enabling robust self-healing under a moving scattering potential. These results clarify the role of SU(2) gauge fields in stabilizing non-Hermitian topological phases and indicate that the proposed model can be realized with currently available photonic, atomic, and superconducting experimental platforms.