Here it translates to "Are you going to ask for more money", but the "for" is omitted in translation. Why is this the case and how can I tell when to drop "pour"?
No "pour" is used simply for the reason that in French "to ask for sth" is not constructed with a preposition in this case.
Il lui a demandé des allumettes.
He asked him for some matches.
Le mécanicien a demandé les clés de la voiture.
The mechanic asked for the car keys.
In other cases "demander" will be constructed with a preposition, but it is never "pour".
Il lui a demandé d'allumer son feu.
He asked him to light his fire.)
Ils leur ont demandé de partir.
They asked them to go away.
When "pour" is found after "demander" it is part of a "complément circonstanciel" and does not introduce an object. This is probably the context in which you found "pour".
- Il l'a demandée pour secrétaire personnelle.
- Ils le leur ont demandé pour s'en assurer, mais ils le connaissaient déjà (le chemin de la gare).
- Le divorce pour faute peut être demandé pour des faits imputables à l'autre époux… (Google books)
- — Qu'est-ce qu'il demande pour cette bicyclette ? — Il demande cinquante euros.
What's he asking for this bicyle? He's asking fifty euros.
- Tu vas demander plus d'argent pour cette bicyclette ? Elle les vaut pas !
In this particular case "pour" means "in return for". Are you going to ask for more money (in return) for this bicyle?
As ever with prepositions, don't expect them to map out perfectly from one language to the next.
Arguments indicating the goal of a verb are marked with for in English (ask for, look for, call for, etc), but are direct objects in French, a trait inherited from Latin (and indeed from the common ancestor of English and Latin. While English developed a preposition to mark those arguments of goal, a close relative like Dutch didn't (ask for something is just "iets vragen" literally something ask).
However marking goal arguments as direct objects is cross-linguistically weird, and English is far from the only Indo-European language that developed a preposition to fill that role. In less formal registers of French, some such prepositions have developed: après in European French and pour in Canadian French (the choice is usually regarded as influence from English).
Je cherchais le mot juste -> je cherchais après le mot juste (EU) / Je cherchais pour le mot juste (CA)
Il te demandait -> Il demandait après toi (EU) / Il demandait pour toi (CA)
However, such an usage is still stigmatised, and as a learner you should use the direct object versions.