Have you checked the system status page in WooCommerce to see if there’s anything not functioning properly?
Besides that you might want to see if it’s actually a WooCommerce problem, or if for example sendmail() is not working. You can either check it in your PHP settings or by simply requesting a password change for your account and see if that email does arrive.
This has been a known issue in WooCommerce, and has apparently arisen when the woocommerce_defer_transactional_emails filter has been introduced. Try and see if that’s the issue by disabling it using this code:
add_filter( 'woocommerce_defer_transactional_emails', '__return_false' );
If the problem persists, and you need your email back up and running asap I can recommend setting up a transactional email service like Postmark. Such services have always been the most reliable to me.