This poem was primarily a paean to chastity and, like chastity itself, was not so popular.

From Shakespeare The World as Stage by Bill Bryson.  Chapter 4 page 88.

We’ve no idea how much or how little Southampton admired the poem dedicated to him, but the wider world loved it. It was the greatest publishing success of Shakespeare’s career—far more successful in print than any of his plays—and was reprinted at least ten times in his lifetime (though only one first-edition copy survives, in the Bodleian Library in Oxford). Written in narrative form and sprawling over 1,194 lines, Venus and Adonis was rich and decidedly racy for its day, though actually quite tame compared with the work on which it was based, Ovid’s Metamorphoses, which contains eighteen rapes and a great deal of pillage, among much else. Shakespeare threw out most of the violence but played on themes—love, lust, death, the transient frailty of beauty—that spoke to Elizabethan tastes and ensured the poem’s popularity.

Some of it is a little rich for modern tastes—for instance:

 

And now she beats her heart, whereat it groans…

“Ay me!” she cries, and twenty times, “Woe, woe!”

But such lines struck a chord with Elizabethan readers and made the work an instant hit. The publisher was Richard Field, with whom Shakespeare had grown up in Stratford, but it did so well that a more successful publisher, John Harrison, bought out Field’s interest. The following year Harrison published a follow-up poem by Shakespeare, The Rape of Lucrece, based on Ovid’s Fasti. This poem, considerably longer at 1,855 lines and written in a seven-line stanza form known as rhyme royal, was primarily a paean to chastity and, like chastity itself, was not so popular.