In some cases, but not all apparently (for some other players), there is a fix that works for me:
hit the ESC key, this may take you to the menu screen where the Load and Save Game screens are greyed out (i.e. they can not be chosen), then hit (left click) the Victory Status button, if it is not greyed out, and after you leave the Victory Status screen, you can now do your turn.
Try it, it may work for you.
Other players have a different problem than I sometimes get. I have continued play of that game for many turns after having the problem (of an AI Race not ending it's turn), and only occasionally having the stuck turn problem. Their game gets totally locked up, I think, and the ESC does not work, for them.
added: It is not always Race 15 that never ends it's turn for me, it has now happened to me with several Races.
But for me at least, the ESC and click on Victory Status button, method has worked many times to keep the same game going. After several turns (or less) that particular Race will stop trying to do whatever causes their unending turn problem, and things go back to normal, until that Race or a different Race has the never ending turn problem.
The difference seems to be that I do not get a frozen game that kicks me out, I can still do things like look at ships and even give orders to them, while that Race never finishes it's turn.
