。
The rough seas left her seasick.
Literal
She [topic-は] stormy-sea [due-to-で] ship [at-に] got-sick.
しけ (時化) is a fishing-and-sailing word for stormy weather at sea — written in hiragana here, though the kanji 時化 (an ateji, or phonetic kanji choice) also exists. しけ originated as 'rough sea' but extends to mean 'poor catch' or even economic 'recession,' all linked by the common thread of bad fortune at sea. The で is causal: '(she got seasick) because of the rough sea.' 船に酔う is the standard collocation for getting seasick — 酔う ('to get drunk, get sick') taking に for the source of the sickness. The same verb covers all motion sickness: 車に酔う (carsick), 飛行機に酔う (airsick).