Fourth playthrough, I had installed Dead Money, and suddenly, Astor wouldn't give me any dialogue other than that Edwards should be put down.
Second playthrough was Legion, so didn't bother with the quest.
On my first and third playthroughs, I had no problems getting Sgt Astor to accept Edwards (passed an Int check to say Edwards wasn't feral). I generally enjoy playing more empathetic, helpful characters, so try to get the best outcomes on most of my playthroughs. I've played through FNV a few times now and have hit a problem with our ghoul soldier friend.
