  We numerically determine the robustness of the lasing edge modes in a
spin-torque oscillator array that realizes the non-Hermitian
Su-Schrieffer-Heeger model. Previous studies found that the linearized dynamics
can enter a topological regime in which the edge mode is driven into
auto-oscillation, while the bulk dynamics are suppressed. Here we investigate
the full non-linear and finite-temperature dynamics, whose understanding is
essential for spin-torque oscillators-based applications. Our analysis shows
that the lasing edge mode dynamics persist in the non-linear domain for a broad
range of parameters and temperatures. We investigate the effects of
perturbations relevant to experimental implementations and discuss which ones
might be detrimental to the stability of the lasing edge mode. Finally, we map
our model onto a photonic model. Our analysis has the potential to shed light
onto the dynamics of a plethora of non-Hermitian systems with non-linearities.
