A lot of factors caused war chariots to cease, actually. For example, take evolution and adaption(this is not science but you know that animals change), and it caused the horses to be taller and stronger, allowing cavalry of 1-2 persons on a horse.
second, weapons, defense, and population grew, so it was easier to group on chariots that had 2-3 horses.
geographical causes too, ceased them to stop, as they could only go on flat terrain, and enemies used this to their advantages by "leading" them into the mountains, where they could pick them off easily.
now, when did the chariots stopped is hard to say. I honestly would say around 3-5 B.C, but I'm not too sure
