Wind does not seem to die before the end

I am having trouble to get a smoke simulation working and it is affected by a wind force field. The smoke setup seem fine. I clearly see it when rendering. There is also a wind force field affecting the smoke and it does it job only at the beginning of the animation. At first the smoke is displaced by the force field as expected. However, the smoke is rising more or less straight up towards the end of the animation. Changing the strength parameter gives expected results, but the wind force still seems to have no strength towards the end of the animation. What could I possibly be doing wrong?