yep,

that's why it's good to have a planet or two continuously building constructors. Bear in mind that certain defensive or offensive modules or your starbases will cost some money.

That's one of those things that's more or less true 'globally' but can be wrong 'locally,' at least in terms of the techs available to you & rival civs and whether you have the hulls to spare to leave big stacks of in the sticks guarding a resource mine.

If you're playing TA with the Thalan tech tree (or able to trade strongly with the Thalans), the starbase defense techs can be very effective until the AIs get to the point where they can build truly monstrous attack fleets. And they're not very good at doing the latter unless you give them bonuses by playing above Tough difficulty.

In fleeted battles, yes, it continues until one side wins.  If you have a stack of tiny hulled ships that aren't in a fleet, the AI has to expend one turn to attack each ship.  It can take many turns to destroy a stack of individual ships, regardless of the attacking fleet's strength.

It's a delaying tactic that's designed to buy time until your own large fleet can arrive to oppose the attacking AI.

Putting a single fighter in the mix can give you the flexibility to counterattack any weak AI ships that are just looking for an easy target.

AS GWS says, it won't work so well if the starbase is in a remote sector.  The time it takes to send engineless tiny hulls out to it would be significant.  In that case, starbase defenses might help for a very limited time. 

As an aside, I've found that leaving my starbases undefended works as an economical alternative.  Only an enemy at war will attack it and I find that I can respond to a threat with a fast huge hulled fighter before most AIs can get to my starbases.  That or send a fleet of constructors after the fighter to retake it if I'm a turn or two too late.

Back when I had fleet battles and such, I used to like to build 2 or 3 undefended military starbases to lure potential enemies into my space.  Once there, I'd surround their fleets with constructors to trap them. The AI would continue to upgrade the trapped fleets, spending valuable resources in the process.

Once I had sufficient contructors to build up ship assists on the starbases.  I'd bring in some fighters.   I'd use the constructors to upgrade the starbases and wipe out the trapped fleets with the fighters.  That had a nice "mwahahaha" value to it too, even if it wasn't particularly efficient.  The down side is that it only works once or twice and the AI quits showing interest in the starbase array.