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. In the case of shows, once you watch 1 episode, the site knows about it and the show will continue showing up on your personal calendar and progress views. So, there is no need to keep it on the watchlist. If you need to keep something around, you can always make a custom list.
For more info, please check out this blog article: