Why do the beavers and the other three children run away when they discover that Edmund is missing in lion the witch and the wardrobe?

Answer 1

they left their home because one of the human children went to the white witch, who they knew would be sending her forces after them to retrieve the other three children. So the beavers take the children to aslan.

Answer 2

Because they figure he has gone to see the White Witch who wants to kill the children, or at least prevent them from fulfilling the prophecy that means her doom, and because the beavers, as accomplices, would be turned to stone.

Answer 3

The beavers and the children run away because they know that the White Witch will have been informed, through Edmund's presence, that the children are now in Narnia. The children are a very real threat to the White Witch's reign, and she will want to kill them before they reach Aslan. Their only choice is to move as quickly as possible to reach Aslan first.

Answer 4

The beavers and the children run away to escape from the danger of being caught by the White Witch's secret police, who are searching for them. They fear they may be captured and taken prisoner if they stay in the area.