Madeleine L'Engle's A WRINKLE IN TIME was rejected 26 times

Did you know that Madeleine L'Engle almost gave up writing when she turned 40 because of discouragement over rejections? "With all the hours I spent writing, I was still not pulling my own weight financially." She discovered, however, that her subconscious wouldn't let her NOT write. 

"I had to write. I had no choice in the matter. It was not up to me to say I would stop because I could not. It didn't matter how small or inadequate my talent. If I never had another book published, and it was very clear to me that this was a real possibility, I still had to go on writing." (Source)

A Wrinkle In Time was rejected 26 times before John C. Farrar of Farrar, Straus and Giroux published it. It ended up winning the 1963 Newbery Medal and became a beloved classic.

Sources:

The Storyteller: Fact, Fiction and the books of Madeleine L'Engle - by Cynthia Zarin on NewYorker.com

Awards & Honors: 2004 National Humanities Medalist, Madeleine L'Engle

Penguin Random House Audio Publishing page about Madeleine L'Engle

Wikipedia pages on A Wrinkle In Time and Madeleine L'Engle (though I notice a lot of conflicting info!)