In addition to pescina's answer, also make sure that under Private data at the bottom, if "Always clear my private data when I close Firefox" is checked.. uncheck it. Also make sure the bottom box "ask me before clearing my private data" box IS checked. This will generally keep everything, but if you decide to clear your cache it will give you the option of what to keep and what to get rid of, so you can keep your cookies.
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As you mentioned, your typical browsing habits are to leave the browser open and open/close tabs as you need them throughout the day. As long as Firefox stays open, you're able to stay logged into sites when you close the browser tab, and then come back to it later.

Closing the browser is not deleting your cookies. Your cookies are saved. Rather, it is your session that expires when you close your browser. Your cookies will always be there until they expire. They're what your browser sends to the web site to tell it which language to display it in and what your preferences are for that site, for example.

So, when you log into a site like Consumer Reports, for example, you can close and re-open tabs as many times as you want and you'll always stay logged in because you haven't closed your browser. Once you close your browser completely, your session has ended, and you must start a new session upon opening a new instance of Firefox.
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