but, from time to time, they do reproduce.
That is something I did not know.
Do you have a link to back the up (I’m not doubting you, I really am curious)
Mules and Hinnies have 63 chromosomes, a mixture of the horse's 64 and the donkey's 62. The different structure and number usually prevents the chromosomes from pairing up properly and creating successful embryos, rendering most mules infertile.
There are no recorded cases of fertile mule stallions. A few female mules have produced offspring when mated with a purebred horse or donkey. Since 1527 there have been more than 60 documented cases of foals born to female mules around the world. There are reports that a mule in China produced a foal in 1984. In Morocco, in early 2002, a mare mule produced a rare foal. In 2007 a mule named Kate gave birth to a mule son in Colorado. Blood and hair samples were tested verifying that the mother was a mule and the colt was indeed her offspring.
http://www.horseforum.com/horse-breeding/mule-reproduction-47843/
There seems to be a problem with disparate numbers of chromosomes between horses and mules, but apparently, this problem is "sidetracked" from time to time.
The question is posed at top of page and you'll have to cursor down about half a page to see the answer.
Same deal with lions and tigers that can mate and create a “liger”
They also have been (rarely) found to be able to reproduce.