This is actually by design. The watchlist is a special “I want to watch” list for you to remember to watch something. Once you watch it, it automatically gets removed. The play is added to your history.
In the case of shows, once you watch 1 episode, the site will update and the show will continue showing up on your personal calendar and your progress view. So, there is no need to keep it on the watchlist. If you need to keep something around, you can always make your own custom list.
For more info and instructions, please check out these blog articles: