Have you checked the settings in Options > Privacy > "Clear history when Firefox closes "- Settings button?

I have the same problem. All my history settings are set to save the history. I even tried a custom setting set the same way, and it still does it. It started with ver. 10 and this is not my only problem since the last version update. I did a complete uninstall and reinstalled Firefox to fix that problem. Not to mention the time I wasted messing with it before I did that. Kind of like right now. Firefox has been flawless for years, all of a sudden these little problems are surfacing. I'm sure they will get it right eventually.

Which security software (firewall, anti-virus) do you have?

Did you make sure that security or cleanup software isn't clearing the history?

If you use cleanup software like CCleaner then check the settings for the Firefox application.