Alright, we have continued to play our save and we think we have figured out what the problem might be. Everything was going fine other than occasional issues with the problem (Unknown Pirates?) until we ended up with a war in the AI. When that happened things was alright until Caek gave an order to a fleet to attack the enemy. It took several turns for the fleet to arrive to attack the enemy, it did so after the player had ended his turn.
What happened is that the fleet went to its destination and attacked its target then after the turn had been ended the game start to process the turn transition and the game saw that the fleet had left over moves after attacking its target but no order to pass or guard or anything. Because of this it had stopped calculating the turn and asked for him to give the fleet orders but he couldn't do so as the UI was grayed out and it had entered a locked state for turn transitions.

We have managed to recreate this issue with multiple fleets as the war has progressed with the problem become more common the more fleets are given orders that end up lasting over multiple turns if their actions result in remaining moves. We also suspect the AI attacking pirate assets or each other is also causing the issue.