This isn't a slowdown due to the game taking longer later in the game.  I'm not a noob whose never played a turn based strategy game before.  It runs fine and turns run smoothly until a specific turn happens and the game for all intensive purpose locks (the frame rate gets ridiculously slow, scrolling the map is choppy, etc.) It never recovers from the slow speed no matter how long I wait.

Like I said in my original post, I've recreated the exact same problem on two separate machines that are running drastically different hardware configurations (one is a desktop the other is a laptop).  It seems to be something in that save game that is causing it to be like this.  I have since restarted a new game and have not seen the issue.