I've noticed that when I'm out at night stars seem to vanish when I focus on them. I assume the reason is physiological and not astronomic. Why does this happen? I would expect that things would be more clear when I focus on them.
When there is little light, the color-detecting cone cells are not sensitive enough, and all vision is done by rod cells. Cone cells are concentrated in the center of the eye, whereas rod cells are very rare in the center (image source):
When you focus on the star, the light is projected close to the center of the retina, where it will hit few rod cells. Thus the star appears to vanish.