I know this has been reported however, I've been able to repeat this process a few times and it could be beneficial.

1st what do I send the developers (save game, error logs ect)
2nd where do I send it to.

Notes

I tested this quite a bit last night, occured well over 40 times. It would almost happen every time a system was envaded more than once per turn. Upon clicking the turn button after such an event nothing would happen. You can still navigate and do all the things you would normally do but your game will not advance. Saving the game leaves it in this mode. However, I noticed if I retired from the game instead it would make a save successfully. Now after you did the retire option and try to reload any saved game, upon reload of the save file the system will CTD (this happens every single time and is 100% reproduceable).

Once I had ships in my orbit protecting my system then the envades would not occur and the amount of times that the Turn button disappeared diminished, but not all together. I haven't tested this but it appeared that when I could click the turn button before battle scene's where over it would disappear.