다가 지다

was doing X and then lost

-다가 marks a change of course partway through, and 지다 is losing a contest: 청나라가 일본하고 싸우다가 집니다 'the Qing fight Japan and then lose', 본능이 이끄는 대로 했다가 짐 'went with instinct and lost'. 지다 has a second sense as the opposite of 뜨다, setting like the sun, which is what 떴다가 지는 것 means of an IP that blows up and then fades.