The NuSTAR X-ray observatory has provided definitive evidence for extremely hard, non-thermal X-ray emission from the massive stellar binary system eta Carinae (eta Car). This emission probably originates from the inverse-Compton (IC) of seed stellar photons by GeV electrons produced by the wind-wind colliding (WWC) shock acceleration. NuSTAR had monitored the emission since 2014 when eta Car experienced a periastron passage of its 5.5-year binary orbit. The observations revealed that the emission declined gradually after periastron, reached a minimum around apastron, and recovered slowly toward periastron in 2020. Interestingly, the non-thermal flux did not increase as the thermal flux did after apastron; it was the highest right after the WWC activity recovery when the thermal flux was moderate. This result suggests less efficient non-thermal activity during the approach of the two stars. The standard WWC shock acceleration models did not expect this result as the WWC thermal plasma should provide seed particles to be accelerated, so the non-thermal emission varies similarly to the thermal emission. We discuss the non-thermal particle acceleration mechanism of eta Car based on these observing results.