If you're a playwright and you submit to theaters, you have a better chance of getting hit by lightning than NOT getting rejected. You have a better chance of winning the lottery (the really big one that covers nine states) than NOT getting rejected. You have a better chance of living forever and not paying taxes, than NOT getting rejected. If you submit work to theaters, you will not only get rejected, there's a really good chance you'll get rejected at the worst possible moment on the worst possible day. Remember the play, P.S. Your Cat is Dead? That's how it works. Your grandmother just died, the bank just repossessed your house, your cat just died, and oh, P.S. your play wasn't "quite right" for the Kennedy Center.
I'm not advocating alcohol as a solution to all of life's problems, but I have found that checking out of the world with a few stiff hits of your vice-of-choice (tequila on the rocks for me) can work fine. Chocolate or your favorite flammable herb works, too. Then get back to writing.
Remembering that playwriting is not brain surgery (no one dies if we fuck up) and hanging out with loved ones can right you. Family and friends are what count in this world, and if you only define yourself by how many productions you list on your CV you're missing a big part of life. Actually, you're missing the big part of life that fuels your art. So get back to the root of things and call your mother, daughter, son, grandmother, best friend--whoever it is who reminds you that you're not defined by theaters and festivals but, as the wizard said, by those who love us. Then get back to writing.
Rejection. There's no dodging it if you're a playwright.
So, how do you handle rejection?