I'm not sure what you mean "it does not work." I look at the ships in range of the starbase on they have boosted defense.

However, I note that there appears to be a one-turn delay in the effect: i.e., if I move a zero-defense fighter into range of a starbase with defense-boosting modules, it has no defense at that time. At the beginning of the next turn, it displays a positive defense value. This works in reverse, too: a ship that's been sitting in range of a defense-boosting starbase will not lose the boost immediately upon leaving the base's area of effect. Only if it ends its turn outside the area of effect will the boost disappear.

EDIT: in light of the post above, I should note that I've only actually checked with ships that already have some limited defense capability. That is, I didn't actually check to see if a ship with no defense of any kind would experience a boost. That may be the problem (and would seem to be a good game-balance solution to the problem of over-tough ships).

Military starbases are boosting correctly. They only boost stats in which you have at least 1 in already. So, for a purely defensive fleet in range of a military starbase, ships with 1/1/1 for attack and 1/1/1 for defense are superior.

-Dewar