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If Nodwick's job (and his life, as an extension) sucks so much, and he can't leave his adventuring party due to contract, why does he consent to being raised over and over again? Resurrection spells require that the spirit be willing to return to life, so why doesn't Nodwick just refuse to return?
I'd guess the contract covers that, too.
It does. In the story It's A Wonderful Afterlife, an angel who has taken pity on Nodwick comes to take him to Heaven and end his misery, but he declines, pointing out that his contract forbids him from moving on unless there is absolutely no hope of resurrection (or until one year after death). The angel tries to find loopholes in the contract and getting Nodwick a better deal by altering reality several times, but each alternate reality turns out to either put the henchman in an even worse situation, or create Hell on Earth for everyone else. Finally, the "Powers What Is" intervene, ordering the angel to stop messing up reality, and that Nodwick appears to be a "destiny sponge" — i.e. if he doesn't take it, the world suffers. Nodwick is surprisingly cheerful about this.
Finding out that your suffering makes a positive difference for the rest of the world would probably take the edge off of being a Butt Monkey.
Why does au Yeager accuse Nodwick of being a liar when Nodwick tells Yeager his name in a world without Piffany. I mean its clear he has memories of leaving Nodwick for dead, but he couldn't have known Nodwick long. Nodwick was neither there first henchman now was he there last. Yeager and Artax don't remember Hedgewick until after Nodwick explains the his backstory, and even then they might just realise that it sounds like something they would have done. Basically I find Yeager remembering Nodwicks name in a world where he was not revived enough times to be mistaken for an immortal to be out of character.
Nodwick has a special talent for making Yeager feel like an idiot, so it's not too improbable that during his short tenure in the group, the alternate universe version of Nodwick said or did something that has stuck in Yeager's mind ever since. (Possibly in a "it's too bad he died before I could work him to death as ruler of the world" way.) And even setting that aside, all the henchmen in that universe are now (un)dead, and "-wick" is a distinctly henchman name, meaning even if Yeager didn't remember Nodwick, he'd automatically assume someone claiming to be a living henchman was lying.