〜を限りに
as of, (with this) as the last time
Time noun + を限りに
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を限りに marks a point in time as the last of something, after which it stops: 今日を限りに、たばこをやめる, "as of today, I'm giving up smoking".
The noun is usually a time: 今日, 今月末, 今シーズン, この試合. The second half is an ending: quitting, retiring, closing, leaving. It's typical of announcements and resolutions: 今月末を限りに閉店いたします, "we will close at the end of this month".
It's close to を最後に, "as the last". Compare までに, a deadline for doing something.
There's a separate fixed phrase, 声を限りに, which means "at the top of one's voice", as far as the voice goes.
Examples
今日を限りに、たばこをやめる。
As of today, I'm giving up smoking.
当店は今月末を限りに、閉店いたします。
This shop will close its doors at the end of this month.
彼は今シーズンを限りに引退する。
He's retiring at the end of this season.
この試合を限りに、彼はチームを離れる。
After this match, he's leaving the team.
彼女は声を限りに助けを求めた。
She cried for help at the top of her voice.