I had this problem and then it went away and was fixed, but is back again now. Downloaded GSX installer again a couple days ago. I'm using FSX: Acceleration.
We haven't done anything that might have any effect on this so, it's not possible that it would be "fixed" or, if it was, there was no problem to begin with, and you probably simply had the zoom setting too wide, so the sim automatically disabled all animations, which is an optimization feature we don't have any control over it.
I confirm that, either you have the zoom setting too wide or, it should be fixed by restarting Couatl before starting GSX. If it really happens only during the 2nd leg of the flight, restarting Couatl won't cause any issues.