I don't ever remember getting the ED-E quest, but I think I did. He died a little later in a fight so it said I failed the quest, but then I died so the game reloaded. I don't have the quest anymore and I can't get it from the Jonson Nash again. ED-E is alive. Any help? Thanks.

You're fine; you never had the quest to begin with. You can get E-DE way before you even know about the quest, and of course if it dies then you can never do the quest. It's just Obsidian's way of saying "Maybe you should reload a save because E-DE is important for a side-quest!".