Topic says it: I've always set firefox to restore my tabs. Recently it's stopped working; only my home page is shown on startup.
Make sure that you do not run Firefox in (permanent) Private Browsing mode.
In case you are using "Clear history when Firefox closes":
Note that clearing "Site Preferences" clears all exceptions for cookies, images, pop-up windows, software installation, and passwords.
"Tools > Options > Privacy: History: [X] Clear history when Firefox closes > Settings " This isn't an apparent setting in the path you indicated
Use "Use custom settings for history" to see all history settings
Did you check the settings for "Clear history when Firefox closes" ?
Can you please just check those settings to verify that you aren't clearing data?
The "Use custom settings for history" selection allows to see the current history and cookie settings, but selecting this doesn't make any changes to history and cookie settings.
You can check for problems with the sessionstore.js and sessionstore.bak files in the Firefox Profile Folder that store session data.
Delete the sessionstore.js file and possible sessionstore-##.js files with a number and sessionstore.bak in the Firefox Profile Folder.
Deleting sessionstore.js will cause App Tabs and Tab Groups and open and closed (undo) tabs to get lost, so you will have to create them again (make a note or bookmark them).