...is due to your browser (the software you use to look at stuff on the web) being set to accept a small file from the site with a unique identifier. If you go away and come back, the site can check if that file is still there to say "yes, this is the person that was logged in before".
These types of files - cookies - can be used for a variety of purposes, not all of which are welcome. For that reason, browser software (chrome, safari, firefox, etc.) has settings that can be used to reject these files. On top of that, some anti-virus software or plugins, or ad-blocking software, can cause your system not to accept these types of files.
So when you say "I've checked my settings", there's no way to know whether you mean your operating system's general security and privacy settings, the security and privacy settings of your browser, or the settings on some other type of software or plug-in that might be the source of the issue.
If you are using, for example, "private browsing mode" in any of various browsers, then persistent login will not work.
If you are using a browser which has a "forget history" mode, then persistent login will not work.
If you are rejecting cookies for whatever reason, persistent login will not work.
For a single browser, there can be multiple answers to the question of why persistent login is not working. Here are some answers for Firefox, for example:
https://support.mozilla.org/en-US/questions/1176200