To drop off means to inadvertently fall asleep. You may have wanted to stay awake so as to complete sending your text message, but you were overcome by drowsiness and fell asleep.
drop offとは、うっかり寝てしまうことです。起きていて携帯メールを送りたかったのかもしれませんが、睡魔に襲われ寝てしまったということです。
When you go over to sleep and drift off this is called to 'fall asleep' if you are apologising for not doing something then you would simply say 'sorry'
I'm sorry I did not reply sooner, it was late here and I was asleep.
I fell asleep before I got your message and couldn't reply.
I hope it's not too late to reply now since it was too late last night.
I'm sorry I did not reply sooner, it was late here and I was asleep.
I fell asleep before I got your message and couldn't reply.
I hope it's not too late to reply now since it was too late last night.
Please forgive me for not replying before I fell asleep.
I'm sorry I did not reply sooner, it was late here and I was asleep.
（返信遅れてごめんなさい。こっちは遅い時間だったので寝ていました）
I fell asleep before I got your message and couldn't reply.
（メッセージを受け取る前に寝てしまい、返信できませんでした）
I hope it's not too late to reply now since it was too late last night.
（昨日の夜は遅かったので返信できませんでした、今の時間遅くなければいいですが）
Please forgive me for not replying before I fell asleep.（返信する前に寝てしまって申し訳ありませんでした）
Sorry, I didn't reply your message earlier. I fell asleep.
Sorry, I fell asleep before I could respond to your message.
"Sorry, I didn't reply to your message earlier. I fell asleep." This sentence expresses to the reader that you apologise for not being able to text them back sooner because you fell asleep.
"Sorry, I fell asleep before I could respond to your message." This sentence expresses to the reader that you apologise for falling asleep before you were able to text back a response to their message.
"Sorry, I didn't reply to your message earlier. I fell asleep."（返信遅くなってごめんなさい、眠ってしまって）
= この文では、寝てしまって返信が遅くなったことを謝っています。
"Sorry, I fell asleep before I could respond to your message."（ごめんなさい、返信せずに寝てしまって）
= この文では、返信をする前に寝てしまったことを謝っています。
Sorry. I dozed off before I got your last message.
I didn't see your reply before I fell asleep last night.
It was late when I got your last message, and I was out like a light.
1.
The expression "dozed off" is another way of saying that one has drifted off to sleep. According to the sentence, this happened prior to receiving the last text message from the other person.
2.
The expression "I didn't see your reply" indicates that the message may have been received after the person had fallen asleep.
3.
To indicate that it was late is reminding the person who sent the message that he/she is in a different timezone. Using the idiom "out like a light" is a casual way to say that he/she had fallen asleep due to it being late and him/her being drowsy.
1.
"dozed off" は「居眠りする」という意味です。この文では、相手からの最後のメッセージを受け取る前に寝てしまったと伝えています。
2.
"I didn't see your reply"（返信を見なかった）は、メッセージを受け取る前に寝てしまった可能性があることを伝えます。
3.
"It was late" と言って、時差があることを強調しています。"out like a light"（ぐっすり眠って）はカジュアルなイディオムです、夜遅い時間だったので寝てしまっていたことを表します。
"I fell asleep mid text"
This phrase is stating that you 'fell'/went to sleep 'mid'/middle/in the process of texting.
"I passed out before I could text back"
'Passed out' is an expression used when someone falls asleep quickly because they are tired.
"I fell asleep mid text"（メールをしながら寝てしまった）
このフレーズでは「メールをしながら寝てしまった」と伝えています。
"I passed out before I could text back"（返事する前に寝てしまった）
'Passed out' は、疲れていて一瞬で寝てしまったときに使われる表現です。
I fell asleep before I could reply!
返事する前に寝落ちしてしまいました！
上記のように英語で表現することができます。
fall asleep で「寝落ちする」「気づいたら寝てた」ようなニュアンスを英語で伝えることができます。
例：
I fell asleep after lunch and woke up at midnight.
ランチのあとに寝落ちしてしまい、起きたら深夜12時でした。
お役に立てればうれしいです。
アメリカ合衆国 
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