。
She kept sobbing without raising her face.
Literal
She [topic-は] face [object-を] without-raising sob continued.
Three structures stack tightly. ~ずに ('without doing') is the formal-leaning negative continuative — 上げる drops to 上げず, then attaches に — a stiffer cousin to colloquial ~ないで. すすり泣く is itself a compound: すする ('slurp/sniffle') + 泣く ('cry'), capturing the wet, hiccupy quality of sobbing far better than plain 泣く. Finally ~続ける layers on the auxiliary 'continue,' so the action doesn't let up. The picture is grief or shame heavy enough to keep her gaze pinned down — and Japanese often uses 顔を上げる ('lift one's face') metaphorically for facing the world emotionally, so the refusal to do so carries weight.