Writing in her new autobiography My Name Is Barbra, Streisand reveals that the song was inspired by some pillow talk she shared with her husband, actor James Brolin. Describing the moment, she remembers Brolin saying, "I don't want to fall asleep," and, when she asked why, he responded, "'cause I'll miss you."
"What a beautiful, poetic thing to say," she writes. "And it captured a moment of complete bliss… physical, emotional, spiritual."
It may sound unlikely that this sleepy moment made the leap from bedtime to Hollywood blockbuster, but songwriter Diane Warren confirmed it in an interview with ABC News in 2018, reporting that she heard Streisand tell the story during an interview with Barbara Walters in 1997.
"I wrote down the title," Warren said. "I didn’t write the song, but I just thought, ‘I don’t want to miss a thing.’ That’s just a cool title, you know."
Having filed the title away for future reference, Warren used it the following year when she was asked to supply a song for the Armageddon soundtrack. She began with the title, "...'cause it was about the end of the world, and what would you say to somebody if you didn't have that much time left? I wanted that urgency, and so I wrote the song, never knowing Aerosmith was going to do it. That was amazing."
She ended up playing I Don't Want To Miss A Thing for Aerosmith frontman Steven Tyler at the Sunset Marquis Hotel in Los Angeles.
“I'm a terrible singer," she told ABC. "So I'm sitting there singing it with him, and then just hearing him learn it with me, it was amazing. I started crying, you know? It was so emotional."
I Don't Want To Miss A Thing eventually became Aerosmith's only Billboard #1 single, and was a Top 10 hit in 28 countries.
"It was so gratifying to see so many people responding to Jim's words," Streisand writes in her book. "Well, no wonder… so did I!"