Для "грубого нарушения договора" я знаю вариант flagrant breach

Для "нарушать срок" МТ много вариантов предлагает, но соединить вместе у меня не получается.

Контекст (нужно перевести с русского): Х грубо нарушали сроки поставки.

X violated ...

Там есть terms of delivery. Их можно violate. Если бы передо мной стояла задача, crudely violate меня бы не смутило.

можно нарушить нормы (договора, закона и т.п.), регулирующие сроки (, в пределах\в течение которых должны быть совершены некие действия)

serious / material breach

про violation - забудьте, это слово подходит для уголовно-правовых нарушений, нарушений прав человека и т.п.

для "нарушений" __гражданско__ - правового характера - чаще breach,

можно также и non-compliance (with the provisions...) и прочее

blatantly failed to meet the delivery deadlines

варианты:
blatantly failed to meet the scheduled delivery dates
blatantly failed to make delivery on schedule

Well, it's OK to say "to be in serious violation of", like they do here
The town has been in serious violation of its federal stormwater permit for the last three years.
https://www.bostonglobe.com/opinion/editorials/2016/06/02/editorial-another-year-another-for-belmont-water-quality/rng2Qvpjdh6rlKK2Ms6OoM/story.html

Как вариант:
X has a record of being in serious violation of the delivery deadlines

The "record of being in" part is borrowed from

And, for reasons given in our report on the UK’s compliance with the UN Convention Against Torture, we think it is unlikely that they can be lawfully deported on the basis of Memoranda of Understanding with the
receiving country where that country has a longstanding record of being in breach of its international obligations regarding torture, in the absence of effective safeguards against abuse, if such effective safeguards were possible.
http://www.statewatch.org/news/2006/aug/uk-jchr-terror-detention.pdf

It is useful also to check with Ofcom whether the company has any
track record of being in breach of its licence terms.
https://www.cips.org/Documents/Knowledge/Categories-Commodities/IT-and-Telecoms/Telecoms/How_to_buy_Telecommunication_Services.pdf