Neo City quests reset every time you level up

Yes they do. I don't see why not.

Because Nexon.

Since NeoTokyo was pre-Big-Bang, I figured they'd just be lazy and copypasta.
Then again, it's also JMS, and they're always stomping away at weird stuff.
No one (that I know of) covers JMS updates regularly, so I really had no idea.

Whenever you have a circlet in your inventory and finish the quest, it ends dialogue without reward and get a message. Probably because it is one-of-a-kind.

Thanks for the heads up.
Didn't realize it was one-of-a-kind.