The effect of the ion wake downstream of grains immersed in a flowing plasma is observed experimentally through the apparent non-reciprocal grain–grain interactions. Here we extend amplitude-frequency response analysis to examine the nonlinear components of the interaction of a dust particle pair aligned with the ion flow. The particle pair is modeled as two forced coupled oscillators, and a new coordinate system is introduced in which the breathing and sloshing modes are linearly decoupled. Multiple-scale analysis is used to derive analytical expressions for the response in the vertical direction for each mode in this coordinate system. By fitting the analytical expressions to experimentally measured response curves, the nonlinear part of the wake-modified particle–particle interaction is determined and identified as the source for the coupling between the sloshing and breathing modes. It is found that the restoring force acting on the downstream particle is more linear, thus stabilizing the oscillations of the downstream grain.