In case you use "Clear history when Firefox closes" or otherwise clear history.

• do not clear the Browsing History

• Tools > Options > Privacy > Firefox will: "Use custom settings for history": [X] "Clear history when Firefox closes" > Settings
• https://support.mozilla.org/kb/remove-recent-browsing-search-and-download-history

Clearing "Site Preferences" clears all exceptions for cookies, images, pop-up windows, software installation, passwords, and other website specific data.

Clearing cookies will remove all specified (selected) cookies including cookies with an allow exception that you would like to keep.

Does updates the files in the sessionstore-backups folder (check the time stamp) and create a sessionstore.js file in the main profile folder when you close Firefox/

You can use this button to go to the currently used Firefox profile folder:

• Help > Troubleshooting Information > Profile Directory: Show Folder (Linux: Open Directory; Mac: Show in Finder)
• http://kb.mozillazine.org/Profile_folder_-_Firefox

My history is marked "Remember History" I do not clear Site Preferences nor cookies. So this problem is not solved.

Does Firefox create a sessionstore.js file in the Firefox profile folder when you close Firefox?

Are there the normal previous and restore files in the sessionstore-backups folder and do the files have a recent time stamp?

previous.js (cleanBackup: copy of sessionstore.js from previous session that was loaded successfully)
recovery.js (latest version of the sessionstore written during runtime)
recovery.bak (previous version of the sessionstore written during runtime)
upgrade.js-<build_id> (backup created during an upgrade of Firefox)

You can use this button to go to the currently used Firefox profile folder:

• Help > Troubleshooting Information > Profile Directory: Show Folder (Linux: Open Directory; Mac: Show in Finder)
• http://kb.mozillazine.org/Profile_folder_-_Firefox

When Firefox starts at the home page, is the History > Restore previous session item available and, if so, does it work? Note that you may need to look at previously closed windows and tabs on the History menu depending on how you exited out of Firefox.

If the history is there but just not loaded, you might have an optional settings file named user.js which Firefox reads at startup and uses to override your previously set preferences. Some third party software (and malware) creates or modifies user.js. You can check for and, if you didn't create it yourself, remove the user.js file following the steps in this article: How to fix preferences that won't save.

Note: By default, Windows does not show the .js file extension. If you see a file named user which has the type JScript, that most likely is user.js. Or you can switch Windows to showing file extensions using the steps in this Microsoft support article: http://windows.microsoft.com/en-us/windows/show-hide-file-name-extensions