at the cost of illness
病気という犠牲を払って
at the cost of one's health
健康を犠牲にして
at the crack [the break] of dawn
明け方に
at [on] the earliest opportunity
機会がありしだい
at the end of one's patience [endurance]
忍耐の限界に達して
at the end of one's tether
体力［気力，忍耐］が尽きて
at the end of the corridor
廊下のつきあたりに
at the end of this story
この話の結末で
at the entrance to a city [a house]
町［家］の入り口で（◆入り口を建物の一部と見るときはthe entrance of a buildingという）
at the expense of one's health
健康を犠牲にして
