Had the same problem. I find that everytime this happens and I reload there are idle ships with turns available. But the turn button comes up and the game kind of stops after you hot the turn button. Some times the ships are aligned with a planet (i.e on the same tile) instead of being stationed in the planet and sometimes there are just standing and idling. So I have started to check whether there are ships with turns still available before hitting the turn button. This seems to solve the problem.

My game got stuck again and after making a pot of chili, I tried cycling through the ships.  The game let me go through the ones with turns left, but it didn't let me give movement orders.  The last ship in the sequence was an old colony ship hidden beneath a planet and not in orbit around it.  Maybe those type of ships are the root cause?

This game also has a big problem with CTDs.  I have the autosave set to each turn now, but have found that it's not enough.  I have to save it every time I take a planet and redo the buildings or I'll wind up doing it again.  

I'm getting tired of redoing the same turns over and over.

Hey, thanks for posting this! I have had this issue as well, much more so post release than I did through all the alphas and betas... I am now able to continue with the game I have. It sucks having to go through all your ships, especially when you have almost 300 of them!, but being able to continue a game that you've put many hours into is worth it in the long run only because I enjoy this game.

Thank you for posting this! It helped me get unstuck! Turns were taking 10 minutes each of micromanagement, so going back to try again and then getting stuck again was a big deal. If this keeps working, you've saved my 88 hour game! /edit 89 hour game, it worked through the next turn!

Thanks for reporting.