usualy you want to parent the eyes to joints as aposed to binding them to the skull. if your binding them you need to go into the component editor (after selecting the verticies (ues the uv texture editor, i find thats faster than marque slecting it in the viewport) and go to the smooth skin tab and turn all the skin weights to 1 to their respective parent bones.

(btw, this looks like an animation problem so this is in the worng forum)