To give up searching for someone or something after failing to find them; to abandon the search (rare/old-fashioned).
大切な写真を何日も探しあぐねた末に、彼は諦めて再注文した。
After searching in vain for the important photos for days, he gave up and reordered them.
重要な書類を探しあぐねているので、もし見つけたら連絡してください。
I'm unable to find an important document and have given up searching—please contact me if you find it.