「[連絡](https://eikaiwa.dmm.com/uknow/questions/32892/)を取ってなかった期間中は[忙しかった](https://eikaiwa.dmm.com/uknow/questions/91169/)」ので、I have been busyと現在完了形になります。
busyの前にveryやsoを付けて、「すごく忙しかった」様子を表現できます。
at workは「仕事で」、on businessは「仕事上、商用で」となります。
「遊びで」は、on pleasureとなります。
例：
I have been so busy at work.
仕事でとても忙しかったんです。
I have been very busy on business.
仕事上とても忙しかったんです。
I have been は I've been に省略することもできます。
keiさんへ
4月のご質問への回答となり、大変恐縮です。
少しでもお役に立てばと思い、別表現を紹介致します。
I have been ... を使いますのは、先の回答者様も
アドバイスされておられますが「過去のある時点から
今までずっと」というニュアンスです。
形は 「have ＋ 過去分詞」で have been となっています。
※分かりやすい例ですと、
I have studied English for 3 years.
（3年間ずっと英語を[学習](https://eikaiwa.dmm.com/uknow/questions/62411/)しています）
などといった例文を目にすることがありますね。
（既にご存知の事柄でしたら、申し訳ありません）
さて、
①の hectic は 、スケジュールが詰まっている時に
「[てんやわんや](https://eikaiwa.dmm.com/uknow/questions/4423/)」「忙殺されている」といったニュアンスで
使う、カジュアルな表現です。
※相手がノンネイティブの方だと、シンプルに very busy の方が
伝わりやすいかもしれません。
②は、ちょっと冗談っぽく「働き蜂のように」という感じです。
日本語でも同じ言い方をしますね。
いずれも、have been としておりますので、every day を
使わなくても、日々多忙だったことはきちっと伝わります。
・・・少しでもお役に立てますと幸いです。
kei さんの英語学習の成功を、心より願っております。
LLD外語学院 学院長 前川 未知雄
"I am sorry I haven't been able to get in contact with you in awhile. I have been so busy with work. I have been working every day."
We usually use the word hectic when we want to explain that we are so busy with work, we don't have the time to do anything else.
For example: Work has been so hectic recently. I am sorry I haven't been able to get back with you.
"I am sorry I haven't been able to get in contact with you in awhile. I have been so busy with work. I have been working every day."
（しばらく連絡できず申し訳ありませんでした。毎日仕事ですごく忙しくて）
仕事が忙しくて他のことをする暇がないことを表す場合には「hectic」を使うことが多いです。例えば：
"Work has been so hectic recently. I am sorry I haven't been able to get back with you."
（最近すごく仕事が忙しくて。連絡できず申し訳ありませんでした）
I'm sorry i have not contacted you, i have been so busy with work recently
I have not contacted you recently as i have been busy with work
I'm sorry' before is a polite way to let them know you are sorry about it
To contact someone is to get in touch or speak to them
So to say 'I'm sorry i have not contacted you, i have been so busy with work recently'
始めの「I'm sorry」は、申し訳ない気持ちを表す丁寧な表現です。
「contact（動詞）」は「連絡する」という意味です。
例：
'I'm sorry I have not contacted you, I have been so busy with work recently.'
（連絡できず申し訳ありませんでした。最近仕事で忙しくて）
"It's been crazy at work" is a way native speakers describe their workload as unusually heavy and that they have been very busy. The use of the word 'crazy' here doesn't necessarily mean it's been bad; this phrase can be used in a good way or a bad way. Eg: "It's been crazy at the coffee shop, we are finally making some money!" or "Work has been so crazy I haven't been able to even eat during the day".
"I have been swamped at work recently" means that you have so much work that you are sinking in it. It can also go with a saying "I've been up to my eyeballs in work"; both are visual ways of describing there is so much work that you are surrounded by it and it is not an easy or comfortable position to be in. EG: "I'm sorry I won't be able to make it home for dinner tonight, I'm swamped at work".
"It's been crazy at work"
（仕事がすごく忙しかった）
- ネイティブが使う言い方です。仕事が多くてすごく忙しかったことを表します。この「crazy」は必ずしもネガティブな意味ではありません。このフレーズはいい意味でも悪い意味でも使われます。
例：
"It's been crazy at the coffee shop, we are finally making some money!"
（コーヒーショップがすごく忙しかった。やっと少しお金になっている）
"Work has been so crazy I haven't been able to even eat during the day."
（すごく忙しくて、昼間食べる時間もなかった）
"I have been swamped at work recently."
（最近仕事で大変なんだ）
- 仕事に埋もれるくらい忙しいという意味です。「I've been up to my eyeballs in work」と言うこともできます。どちらも、仕事に追われて、大変なことを視覚的に表します。
例：
"I'm sorry I won't be able to make it home for dinner tonight, I'm swamped at work."
（夕食に間に合わなくてごめん。仕事が山のようにあるんだ）
I'm sorry I haven't been in touch. I've been quite busy with work.
I have been so busy with work, that's why I have been so quiet.
When you want to explain to someone that you have not been in contract because you have been busy with work lately, then you can say it in the following ways:
-I'm sorry I haven't been in touch. I've been quite busy with work.
-I have been so busy with work, that's why I have been so quiet.
最近仕事で忙しかったので連絡ができなかったことを説明したいなら、以下のように言えます：
-I'm sorry I haven't been in touch. I've been quite busy with work.
（連絡できなくてごめんなさい。最近仕事で忙しくて）
-I have been so busy with work, that's why I have been so quiet.
（最近仕事で忙しくて。だから連絡できなかったんだ）
Work has been piling up recently. There was so much to do!
hectic is another word for "busy", but it means being extremely busy. It is a phrase that is commonly used by people.
"piling up" is another word for "too much work". It means that the work doesn't stop.
You can also add an "I'm sorry I wasn't able to get in touch, work has been hectic lately." to show an apology and being polite.
Hope this helps!
「hectic」は「busy」の別の言い方ですが、「hectic」はものすごく忙しいという意味です。よく使われる表現です。
「piling up」は、仕事が多すぎることを表します。仕事がたまるという意味です。
また、
"I'm sorry I wasn't able to get in touch, work has been hectic lately."
（連絡できずごめんなさい。すごく忙しかったので）
と丁寧におわびの気持ちを表してもいいです。
参考になればと思います。
If you want to explain to someone that you haven't contacted them in a while because you have been busy at work, you can say:
"I've been very busy at work lately."
"Work has kept me very busy lately."
「仕事が忙しくてしばらく連絡ができなかった」と説明するなら、次のように言えます。
"I've been very busy at work lately."
"Work has kept me very busy lately."
（最近仕事が忙しかった）
To someone you haven't contacted in a while, you want to say something like "I was busy recently every day with work." There are a couple of suggestions above for that scenario.
しばらく連絡をとっていなかった人に、"I was busy recently every day with work." （最近仕事で毎日忙しかったんだ。）のように言うといいでしょう。またこれらの例も使ってみるといいでしょう。
"I have been so busy with work recently." is telling the person that they did not have any time to do anything else because they have been that busy at work.
"I have been so busy with work recently."（最近仕事で忙しかった）
は、「仕事が忙しくて他のことをする暇がなかった」と伝えます。
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