She kept on crying.

Literal

She [topic-は] kept-crying.

The compound verb 泣き続ける pairs the masu-stem 泣き with the auxiliary 続ける ('continue'), producing a one-word 'keep on crying.' This pattern is hugely productive: 食べ続ける ('keep eating'), 走り続ける ('keep running'), 考え続ける ('keep thinking'). The construction emphasizes continuation by the subject's own activity, and contrasts with state-focused alternatives like ずっと泣いていた ('was crying the whole time') which lean on the ~ている of ongoing state. 続ける takes a transitive feel — the subject is actively continuing the action — even when, as with crying, the doer doesn't fully control it.