Sounds like your Firefox is set either to clear the cache or not keep cookies upon closing. "Cookies" (in this context) are small files that keep site-specific information (like login session status) but also can be used by advertising companies to track people around the web.
You can change the settings as follows:
1. Select Options from the "Hamburger" Menu:
2. On the left hand side of the options window, select "Privacy and Security":
3. Make sure "Clear history when Firefox closes" is not ticked.
4. Make sure "Accept cookies and site data from web sites" is selected. To limit tracking (without installing extra addons), I make sure that "Accept third-party cookies and site data" is set to "From Visited". This means that only the sites you actually visit are allowed to store cookies in your browser's cache.
Hopefully this helps solve the problem for you.
Note that you do not need to have your browser remember logins or passwords for you for this to work. That setting allows the browser to store the username and password of a site so that when the site prompts you to log in, the browser can fill those fields automatically. I never have this enabled, especially on my laptop, just in case somebody can get access to it.