wither on the vine

今日も「英語で楽しむ寺田寅彦」に出てきた慣用句を取り上げます。
Suppose there arises a rumor that a major earthquake will strike at three o'clock tomorrow morning. If, say, thirty percent of the influential men in the neighborhood know for certain that such precise earthquake prediction is still impossible, the number will wither on the vine.
"wither on the vine" は単に "wither" でも通じるようですが、"wither on the vine" が慣用句であることを辞書で確認します。
・Cambridge Dictionaries Online: If something withers on the vine, it is destroyed very gradually, usually because no one does anything to help or support it: There was some debate as to whether the benefit scheme should be withdrawn or simply allowed to wither on the vine.
・American Heritage Dictionary of Idioms: Fail to come to fruition, as in This building project will wither on the vine if they don't agree on a price. This expression alludes to grapes shriveling and drying up because they were not picked when ripe.