System and method for attenuating the drying of ink from a printhead during periods of printer inactivity

A capping station is configured for storing printheads during printer inactivity to preserve the viscosity of the ink in the nozzles of the printheads. Each capping station has a receptacle, a planar member having a shaft that moves bidirectionally within an opening in a floor of the receptacle, a source of cleaning fluid, and a vacuum source. A controller is operatively connected to actuators to move the receptacle so a seal on an upper wall of the receptacle engages a printhead housing and to move the planar member within the receptacle. The controller also operates a pump to move cleaning fluid through the receptacle and to operate the vacuum source to pull ink from the nozzles of a printhead to the faceplate of the printhead. The planar member is moved proximate the faceplate so the ink forms a film that preserves the viscosity of the ink in the nozzles.