。
She was dozing the whole time.
Literal
She [topic-は] that interval continuously dozing was-doing.
その間 ('during that interval') ties the action to a previously established stretch of time — 'that' meeting, 'that' speech, 'that' lecture, whatever the surrounding context made clear. ずっと ('continuously, the whole way through') reinforces unbroken duration. 居眠りをする ('to doze, to nod off') specifically describes sleeping while seated and supposedly attentive — the kind of sleep that happens at desks, in classrooms, on commuter trains. Japanese has a specific word for this for good reason: dozing in semi-public settings is widespread and culturally tolerated as a sign of how hard one has been working.