Series vanishes from watchlist after I’ve watched an episode

Hi,
Like the user above said, that’s the way the watchlist is intended to be.
If you have any questions about the watchlist, please read this: What is the Watchlist? What kind of items should I add to it? - Support / FAQ - Trakt Forums

If you don’t want the items removed after watching them, you can use a custom list. Those kind of lists do not remove the items once you have watched them.