When Baron Nashor dies, does his battlefield also disappear?

When Baron Nashor dies, the Baron Pit battlefield token does not disappear.

While Baron Nashor's "When you play me" ability is responsible for adding the Baron Pit to the board, the token exists as an independent game object once created. There is no rule that causes a battlefield token created by a unit to leave the game when that unit dies or leaves the battlefield.

As noted in the RiftJudge FAQ #9403, the Baron Pit simply persists as a battlefield location that units can move to from anywhere.