I don't know if this has been identified but I have seen several posts about the game getting hung up between turns. This recently happened to me in one of my games and I was able to go back to an autosave and fix the condition which caused to cause the wait indicator to hang. Here is what I did
To prevent the AI from colonizing in my influence I blockaded the planet I assumed he was going for with ships in every hex around the planet. Once I hit end turn the game got stuck on the wait between turns. I went back to the autosave and instead of blockading the entire planet i left one hex open on the opposite side of the planet so it would take 2 turns for him to get there hit 'turn' and no game freeze. I have done this a couple times to ensure that it is an issue with the pathing the AI chooses and its stubbornness to change if its first target isn't available.
Well hopefully this helps, now back to my game.