Aoi is a hard-up student, so she can't afford something that expensive.

Literal

Aoi [topic-は], working-student is-[because-から], such high-class thing, cannot-hold is.

苦学生 (くがくせい) is a specific cultural concept — a student working their way through school under financial hardship, paying their own way. The potential 持てない is from 持つ ('to hold, have, own'); in this context it means 'cannot afford/cannot have'. Note how the noun 'such a high-class thing' is left dangling at the end without an explicit object particle — an intentional elision that gives the sentence a conversational, slightly exasperated feel. The copula です at the end is polite but the content and rhythm are casual-conversational.