The Dungeon World rules do not appear to be explicit about whether a spell is lost if you rolled a 6- to do so, while it is explicit when it is an option when you roll a 7-9:
Casting a spell involves calling on a deity, chanting, waving ones hands, invoking mystical forces, and so on. To cast a spell you will usually make the cast a spell move. On a 10+ the spell takes effect, on a 7–9 the caster finds themself in trouble and must make a choice, but the spell is still cast. Some spells are ongoing—once they’re cast they continue to have effect until something ends it.
One option on a 7–9 result is to have the spell revoked or forgotten. A spell that is revoked or forgotten is still known, but no longer prepared, and therefore no longer castable. When the caster next Prepares or Communes they may choose the same spell again.
(source: Dungeon World SRD)
A wizard's Cast a Spell move is also not explicit about the spell being lost if you fail the roll, but does use the following wording to trigger the move:
When you release a spell you’ve prepared, roll+Int.
(source: Dungeon World SRD)
So, does failing to cast a spell cause the spell to be revoked or forgotten for the day?
Best Answer
No, you don't automatically lose the spell on a 6−. But you might.
It doesn't explicitly say whether you lose the spell, and that's on purpose. Missing on Cast a Spell gives the GM a chance to say something about what happens. That might include forgetting the spell or having it be revoked, but not necessarily. What happens next is what the GM says happens next, and that's all. If she doesn't say the spell is lost, then it isn't.
If you haven't got to the section on the rules for the GM, this will make more sense then. (If you're a player and your GM hasn't read the GM section yet, that's something your GM should do before running another session. Too many new Dungeon World GMs skip it because they assume it's just advice, but it's actually the rules for the GM player, and about 90% of the game!) The GM's rules are pretty explicit: you can do one thing, or another thing, but losing the spell and something else that's unrelated to losing the spell would take two GM moves, and she only gets one on a miss.
How player moves work is explicit too: do what the move says. Losing the spell is optional on a 7–9, and Cast a Spell doesn't tell you anything extra on a 6−, so it's not automatic in any way on the player's side of the rules. On a miss it's all up to the GM what happens, but the GM has rules to follow when deciding that.