No, the special abilities of BBs, AA guns, and subs all take place before the battle actually begins, and only once during an attack

Actually that is not entirely correct.

Subs DO get to use their special ability in subsequent rounds.

On page 16 in the manual it states that you are to repeat steps 2-6 each round. And it also says that units returned to the gameboard cannot reenter combat.

The sigificance of this is obvious if you look at the beginning of page 16.

It says:
Return all antiaircraft guns to the gameboard as well as battleships that conducted shore bombardment. Do not remove submarines from the battleboard.

Opening fire is part of step 2 of the combat and thus has to be repeated every round. However by following the above rule in step 3, battleships (that did shore bombardment) and AA guns must be returned to the gameboard the first time a combat reaches step 3.
But that still leaves submarines to go thru step 2 once again and for as long as they live in the combat.

• Kvik