In season 7 episode 6, "Beyond the Wall",
Some rangers fight with a small group of wights led by a white walker. When the white walker is killed, all the wights but one are disintegrated.
Obviously, this conveniently serves the scenario.
I found a few interesting justifications on the web, one of the most convincing perhaps being that the Night King would send one of its own wight with wights teams to see through its eyes (or orbits at least…).
But did the showrunners themselves provide an explanation on how this wight could still be animated?