@ottersteeth
Although @Zannarii is close, his reply isn't entirely correct.
The fort will re-spawn the skeletons at the cannon towers as soon as all of the crew have died.
If you are solo it will re-spawn the tower skeletons straight away otherwise it will re-spawn them when all crew members are on the ferry or otherwise off the island itself. This includes a lookout staying on the ship parked at the fort. Someone needs to be on land.
Keeping the skeletons in the cannon towers alive works in your favour as they will fire upon any approaching vessel and give you fair warning of other arrivals.
So, as Zannarii suggests, park in a safe place rather than taking them out. Otherwise they will fire upon your vessel before you get a chance to spawn again.
As Zannarii also said, you need to keep fighting the waves of skeletons until the captain is defeated.
He will drop the stronghold key and that action would also de-spawn the rest of the skeletons and the tell-tale cloud above the fort will dissolve with a final glimmer of green before disappearing.
edit: As for the fort resetting. No, it won't do that for three hours and now that too has been effected by the skeleton ship raids. Either one or the other will appear active at any given time, not both.