The rabbit's association with the pagan rebirth festivals of Christmas and Easter seems to date back to ancient Mesopotamia and Syria 3,000 thousand years ago, when, according to www.exploregod.com, the hare came to be adopted as a symbol of death and rebirth.
Over time the associations made with hares shifted to rabbits because they have many of the same characteristics.
This association with death and rebirth may be why rabbits were depicted on gravestones in the Greco-Roman world. Early Christians appropriated the rabbit as a symbol on their gravestones as well. As you can see, there has been a longstanding connection of hares and rabbits with death and rebirth—or in the Christian sense, resurrection.
Moreover, in the Greco-Roman world, rabbits were also associated with lust and sexual excess. This idea has endured—something we can see in Hugh Hefner calling his playmates “bunnies.” A connection between rabbits and sex was obvious, given how often rabbits were caught engaging in sexual activity and giving birth. Even today, we’ve likely all heard the phrase “breed like rabbits.”
... Given this association and the arrival of spring in the Northern Hemisphere—which signaled the rebirth of the earth after winter—hares and rabbits became symbols of fertility in pre-Christian Europe.Reference: Richard Cavendish, ed., Man, Myth, & Magic: The Illustrated Encyclopedia of Mythology, Religion, and the Unknown (New York: Marshall Cavendish, 1983).