Looking on the internet deeply has found these results:

I apologize is the most popular phrase on the web.

i do apologize 1513,000 results on the web	I apologize 124,600,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
I do apologize, ma'am, but the guests directly overhead, a rather large gentleman, broke his toilet. I do apologize, little lady, but it's better for you if you don't see where we're going. Once again, I do apologize for breaking said trust. I do apologize for any inconvenience. I'm so sorry to have kept you waiting, your Lordship. I do apologize, please forgive me. And I do apologize for that. I do apologize for these consent forms. I do apologize for this necessary precaution, Miss...	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

i do apologize

1513,000 results on the web

I apologize

124,600,000 results on the web

More popular!

I do apologize, ma'am, but the guests directly overhead, a rather large gentleman, broke his toilet.
I do apologize, little lady, but it's better for you if you don't see where we're going.
Once again, I do apologize for breaking said trust.
I do apologize for any inconvenience.
I'm so sorry to have kept you waiting, your Lordship. I do apologize, please forgive me.
And I do apologize for that.
I do apologize for these consent forms.
I do apologize for this necessary precaution, Miss...

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.