The only thing I have to add to kryo's post, is that the pathing AI is not smart enough to plot multi-jump courses that include phase sabalizers. I.E:
a-----b------c-------d
say you are at planet A and want to get to planet D. Planet B and D have stabilizers, but A does not. If you just tell your fleet to move from A to D. They will jump to b, jump to c, jump to d. In order to jump directly from b to d, you must jump the fleet to b, and then tell them to jump to d upon their arrival. It was because of this fact that I also thought they didn't work at first.
