Nodes remain permanently marked on the physical card. They’re not removed as it becomes a new object or as the game ends.

If an object without nodes becomes a copy of an object with nodes, the copy has no nodes. A cost to mark one of its nodes can’t be paid.

If an object with nodes becomes a copy of another object with nodes, the nodes on the physical card that’s the copy will be marked if the legacy abilities it gains instruct you to mark a node. Thus far, this ruling applies only to the case where one Gold Mine becomes a copy of another Gold Mine.