I don't understand what that means. What is しちゃア and the last い ?
I assume it means something like :
I can't stop drooling if you keep making that desesperate face.
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そんなに絶望的｛ぜつぼうてき｝な顔｛かお｝をしちゃア、妾｛わらわ｝の涎｛よだれ｝が止｛と｝まらなくなっちまう じゃあ 「なィかい♪」
It could be said formally like:
そんなに絶望的｛ぜつぼうてき｝な顔｛かお｝をしたら、妾｛わらわ｝の涎｛よだれ｝が止｛と｝まらなくなってしまう では 「ないかい♪」
I couldn't stop drooling if you keep making that hopeless/desperate face. Don't you think so?
I couldn't stop drooling if you keep making that hopeless/desperate face,right?
妾｛わらわ｝ or 私｛わらわ｝ is a word that a woman calls herself humbly in the feudal period in Japan.
It looks like manga-style sentence attempting to represent the way people speak. I suspect the しちゃア is a contraction of してしまう, which is often contracted to しちゃう in everyday speech, in a dialect where that last う becomes an ア sound.
The last い simply looks like one of the many occasions where the regular か for questions becomes かい in speech.
Your translation might work if the speaker is the concubine/mistress (妾), but without further context, I'm hard pressed to understand why a concubine (several concubines?) would be drooling over someone looking especially down.