The Dr. Seuss bibliography lists a number of books that were published posthumously. While I do realize that it's not uncommon to have posthumous works, several of these books are apparently quite old. For example, What Pet Should I Get? is believed to have been written in the 1950s or 1960s, and Daisy-Head Mayzie was written in 1973. Given that Dr. Seuss was publishing books until 1990, why did it take so long to publish these?
For My Many Coloured Days, probably because he didn't find a good enough illustrator.
My Many Coloured Days, apparently the only posthumously published Seuss work to be written entirely by the man himself, was written in 1973. But the author wanted to find a great colour artist to complement his writing for the story, and apparently he never found one that satisfied him.
Accompanying a manuscript Dr. Seuss wrote in 1973, was a letter outlining his hopes of finding "a great color artist who will not be dominated by me." The late Dr. Seuss saw his original text about feelings and moods as part of the "first book ever to be based on beautiful illustrations and sensational color." The quest for an artist finally ended—after the manuscript languished for more than two decades—at the paint brushes of husband-and-wife team Steve Johnson and Lou Fancher
-- Seussville (official website)
For What Pet Should I Get, the manuscript was only discovered after his death.
As noted by Matt Thrower in a comment, Seuss himself never sent What Pet Should I Get to a publisher. It was rediscovered after his death in a box of old notes, together with projects he'd classified as failures. Apparently he'd thought it wasn't worth publishing:
After Theodor Seuss Geisel, better known as Dr. Seuss, died in 1991, his widow, Audrey Geisel, decided to renovate their hilltop house in La Jolla, Calif. She and an assistant cleared out his office, donating most of his valuable illustrations and early drafts to the University of California, San Diego, and stashing some doodles and abandoned sketches in a box.
It wasn’t until October 2013, when they decided to have the rest of his notes and sketches appraised, that they closely examined the contents of that box. They found a set of brightly colored alphabet flash cards, some rough sketches titled “The Horse Museum,” and a manila folder marked “Noble Failures,” with whimsical drawings that he had been unable to find a place for in his stories.
But alongside the orphaned sketches was a more complete project labeled “The Pet Shop,” 16 black-and-white illustrations, with text that he had typed on paper and taped to the drawings. The pages were stained and yellowed, but the story was all there, in Dr. Seuss’ unmistakable rollicking rhymes. [...]
Through painstaking work and a meticulous, almost forensic reconstruction of Mr. Geisel’s creative process, those abandoned pages have yielded an unexpected new Dr. Seuss book, now called “What Pet Should I Get?” When Random House publishes it on Tuesday, with a first printing of one million copies, it will add a surprising coda to Dr. Seuss’ sizable canon.
Other works were republished or rewritten by others.
Looking through the list of posthumous Seuss stories, it seems as though:
- Oh, Baby, the Places You'll Go! (sounds more like a pop song, doesn't it) was mostly written by Tish Rabe as an adapted version of Seuss's original Oh, the Places You'll Go!;
- Hooray for Diffendoofer Day! was put together by Jack Prelutsky based on incomplete notes by Seuss;
- The Bippolo Seed and Other Lost Stories and Horton and the Kwuggerbug and More Lost Stories were only republications of stories which had already been published during Seuss's lifetime.
The only remaining mystery, then, is Daisy-Head Mayzie. I haven't been able to find any information on why this was only published posthumously.