This is the slogan of (and registered trademark of since 1994) the Children's Defense Fund. The CDF's president and founder, Marian Wright Edelman, has contemplated suing the GOP for appropriating the phrase, though I think she has dropped the matter.

"If plagiarism is the sincerest form of flattery, I am more than happy to be flattered that the theme of the Republican National Convention's opening night on Monday is "Leave No Child Behind"--the four words that constitute the Children's Defense Fund's trademark. ... "Leave No Child Behind" should be more than the theme for an evening at a convention or even a trademark for an organization."