So many Shih Tzu eat pooh, as well as other breeds. It's pretty easy to tell they're doing it when they jump up in your lap and try to give you kisses too! YUCK!
Four of my five did it when they were young, but have (pretty much) outgrown it now. I tried the pills and other recommendations with the first one, and none of that worked. Luckily she outgrew it shortly after she turned one year old. (Oh, and she never ate her own, just my other dogs.)
Other than the grossness to us (humans), it really isn't harmful (as long as it's a "healthy" (???) poop! All mommy dogs do clean up a