Signing in starts a session. If the developer of the site hasn't changed the default (most don't), most web servers time a session out after 30 minutes of no input from the user. (Some sites [like Android Central] have a "keep me logged in" button, which sends a cookie to your browser, so the next time you go to the site you're automatically logged in again.)
(From the site's viewpoint, you never stay connected, you connect, download the page, then disconnect - but the session stays active on the site for 30 minutes after that, and resets to 30 minutes every time you send something to the site. In the case of Wish, that could be tapping a different header or looking at details for an item.)