What accounts for the disappearance?
Cells that transduce light into visual system voltage signals populate the posterior (rear) of the retinas of our eyes. Light transducing cells of the retinas are classified into two categories named for their shapes: rods and cones.
Cones populate a relatively central region of the retina. When you look at an object you are bringing light from the object onto the cones for transduction of the energy from the object. Cones operate in what is called photopic or higher intensity vision. Cones have a higher intensity threshold for firing than rods. The energy from some stars will be of sufficient intensity for the cones to respond.
Rods populate the periphery. Rods operate in what is called scotopic or low intensity vision. Rods need less intense light to fire. The light from some stars will be sufficient to produce a rod response, but not a cone response.
When you first see stars that appear dim in your peripheral vision, rods are transducing the light from the stars. When you look directly at the stars, the transduction must be done by cones, but the intensity of light from some stars is below the threshold for cones to respond.