There seems to be more than one problem currently in 0.55 GC IV Alpha.
One problem is that an AI Race sometimes never finishes it's turn , probably it's movement subprogram for one of it's ships has a problem generating a legal order (according to GM Carrie), and so the next turn never happens.
I have found a solution to being to continue your turn, for this problem.
Hit the ESC key, this will take you to main Menu, the Load and Save buttons are greyed out and can NOT be chosen.
However, the Victory Status button is not greyed out and CAN be chosen by left clicking on it, and when I leave the Victory Status Screen, I can now do my turn normally. I have been able to keep playing my game even after having this problem several times, and then using this method to get out of it.
After a while the AI Race seems to stop having whatever problem it was having. In my case it was always the same Race that had the problem, i.e. the Mimot, However, later in the game (or in your game) it might be a different Race, having a similar problem. The problem did not start happening to me until I moved a ship into Mimot territory and meet them.
The second problem seems to be the game freezing or locking up when the Player moves their mouse cursor over the resources in the very top line on the screen and then the Game freezes. Since this problem has never happened to me, I am NOT aware IF the above method will help against this problem (I doubt that it will help). That problem is being looked at by the GMs.