Does Elder Dragon's passive stop after Elder leaves the board?

In a game, my opponent had Elder Dragon on battlefield 1 and Volibear on battlefield 2. I killed Elder Dragon on battlefield 1, trading because its ability killed my unit even though I had more Might. I then moved in to start a second showdown against Volibear with a unit that had more Might.

My opponent argued Elder Dragon's effect stays for the whole game once played. Does Elder Dragon's passive end once Elder Dragon is no longer on the board?