。
She got fired on the grounds of frequent absences.
Literal
She [topic-は] absence-prone is [on the grounds that-という理由で] became-the-neck (got-fired).
首になる ('to become a neck') is the standard idiom for 'to get fired,' tracing back to old metaphors of having one's head severed from a position of duty — modern usage is matter-of-fact and not graphic. The sentence stacks two grammar pieces: 欠勤がち uses the suffix ~がち to mark a habitual tendency with a slightly negative tilt, and という理由で packages the entire preceding clause as the official cited reason for what follows. Notice how Japanese loads the cause first and saves the consequence for last — the listener hears 'absences-prone, that's the reason, fired' — the reverse of English, where 'fired' usually leads.