“He has been nursing that drink all night!”
To nurse a drink is to drink it little by little. Someone might nurse a drink when he does not want to drink too much alcohol, or does not want to spend much money on drinks. (It doesn’t have to be an alcoholic drink, though.) Or maybe he is just not thirsty!
「彼はそれを飲むのに一晩かけそうだね。」
飲み物を「nurse」するのは「ちょっとずつ飲む」ことです。お酒を飲み過ぎないようにするとか、飲み物にお金をかけたくない時にします。（お酒以外の飲み物でも使えます。）あるいは、ただ喉が渇いていないだけかもしれません！
