Based on his reply, I didn't think there was much hope.
His response didn't give me any cause for hope.
この場合、次のような言い方ができますよ。
ーBased on his reply, I didn't think there was much hope.
「彼の返信を踏まえると、脈がないように思う」
there is not much hope で「脈がほとんどない」と言えます。
ーHis response didn't give me any cause for hope.
「彼の返信は私に脈があるという根拠を与えなかった」＝「脈なしに感じた」
このようにこの「脈」は hope を使って言うと良いでしょう。
ご参考まで！
カナダ 
