It is a common way to obtain ion-ion plasmas from pulsed electronegative discharges. The pumping pulse can excite ion oscillation at the early active glow stage of a pulsed electronegative discharge. To study the ion oscillation and its influence on the self-sustaining condition of the discharge, a global model was developed to describe the interaction between ion oscillation and a small amount of electrons in a low-pressure ion-ion plasma. A parameter r was introduced in this model to describe the momentum residual/loss of the electrons after the collision with the electrodes. It was found a critical value r=rc that differentiates two electron loss mechanisms. Another critical value r=4rc determines two different threshold of the electron density growth. Thus, the threshold of the electron density growth is non-monotonously depend on r. Therefore, there might be a gap existing in the parameter space of the self-sustaining condition. The above result has been examined by a particle-in-cell simulation with Monte-Carlo collision (PIC-MCC).