I managed to slay an elite with invulnerable minions, but half of his minions retained invincibility... frustrating to say the least.

It was a kind of monster that burrowed when not active, so it may be that the fact that they were burrowed when I slew the elite that prevented them from dying. I was also out of range of them... but please look into this. It essentially requires you to restart your game, erasing any progress you made toward the next waypoint.