Current sheets propagating in a parallel-plate accelerator are found to arrest their motion at an electrode-insulator junction, and there to lapse into stable, quasi-steady discharges. Kerr-cell photography, magnetic and electric probing, and terminal voltage measurements indicate that these stabilized discharges accelerate gas through themselves as long as gas from the prefilling of the discharge chamber is available, after which enhanced erosion of insulator and electrode material appears. To supply fresh gas to the stabilized current zone with a minimum of delay, a shock-tube gas injection technique is used. Even with this procedure, it is found that the current must be driven for hundreds of microseconds before a quasi-steady gas flow can be established in contrast to the tens of microseconds required for electrodynamic stabilization. This quasi-steady flow mode, characterized by both current pattern and gas flow stabilization again is observed to provide substantial acceleration of the inlet flow.