In GalCiv 2 Dread Lords, I complained about the lack of defensive ability for starbases. After upgrading a starbase to max (including researching all techs to do that), they were not well suited to their own defense. Fleets could be made that could kill a fully upgraded starbase. It was better to keep a fleet on the same tile to defend them... if you even bothered.
It became worse in Dark Avatar when the combat system got changed and starbases did not get improved to take advantage of it. The changes was from all ships being restricted to 1 attack per round to as many attacks as the ship had weapons (so a ship could kill multiple ships per turn). Starbases never got more attacks. Likewise, the changes to defenses was from defenses working at full power for every attack (so if a ship had a weak attack, it would practically be useless against a well defended ship) to each attack would weaken the defenses of a ship to 0. Starbases didn't get stronger defenses. They became vulnerable to fleets of many ships as they couldn't kill them quickly and their own defenses could be weakened to 0. Further more, ships got even larger, so you could eventually build huge ships that could out class any starbase combat wise, let alone what could be done with fleets.
It became even worse in Twilight of the Arnor. You could now add HP boosting modules to ships. You could add fleet modules to ships (for both attack and defense). Some of the tech trees got remodeled in such a way that some starbase modules got denied to some civilizations. Hell, in some cases it looked like it was remodeled deliberately to have some modules harder to get access to (and became nearly useless by the time you got them).
Overall, I found that starbase defenses were not worth while beyond the basics. If you went for the early bird advantage, it might be useful for a while (if you got it just right, enemy ships would attack on mass and be destroyed in a futile attack against a tough nut). Ultimately, I found that it was best to use ships to defend starbases, namely mining starbases for galactic resources and economic starbases for planets. I found influence starbases to be useful for a time, but it was something to be disposed of once I finished culture flipping a planet or securing the influence in a region through other means. Military, well, I never mastered their use, and many of their modules were the ones that were made harder to get in Twilight. Terror Stars, its best to forget about them.
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In GalCiv 3, the ability to have fleets team up with starbases is a nice boost. It is also a nice boost that fleets with starbases (or planets or shipyards) can exceed normal logistics early in the game (it is 40). Further more, since sensor ranges don't have a limit in this game, it is possible to see attacks coming (and do something about it). It seems that stardock has continued to leave them the support role. They can be defended, but they can't be expected to defend themselves. What advantages they offer is the real reason why you build them.