Deploy the Fleet: Action : Damage this objective to reduce the cost of the next Capital Ship unit you play this phase by 1.

It seems like there is no reason you couldn't use the action multiples times, obviously until the point that you blow it up.

On the contrary, do cards such as Defense Protocol ( Reaction: After your draw phase begins, reduce your reserve value by 1 (until the end of the phase) to deal 1 damage to a target unit.) not allow you to use the ability multiple times because it is a Reaction, not an Action?

That is correct. A reaction or interrupt can only be used once per triggering condition. Actions can be used repeatedly unless they say otherwise.

One thing to watch out for though. Since each activation is a seperate Action, your opponent has the option for an Action after each activation. If you are playing a Rebel player, they might Rebel Assault the objective when you get it to 2 or 3 damage left if you needed those last few resources to bring out that Capital Ship. Plan accordingly and beware.