In a recent paper, a scheme for inserting and extracting high brightness electron beams to/from a plasma based acceleration stage was presented and proved to be effective with an ideal bi-Gaussian beam, as could be delivered by a conventional photo-injector. In this paper, we extend that study, assessing the method stability against some jitters in the properties of the injected beam. We find that the effects of jitters in Twiss parameters are not symmetric in results; we find a promising configuration that yields better performances than the setting proposed in [14]. Moreover we show and interpret what happens when the beam charge profiles are modified