Did you check on the about:cache page that the disk cache is used and working?

In case you use "Clear history when Firefox closes" make sure not to clear the Cache.

about:cache shows,

Number of entries: 16249 Maximum storage size: 358400 KiB Storage in use: 316690 KiB

for disk. That looks in use.

The "Clear history when Firefox closes" is not checked.

Does Firefox create a sessionstore.js file when you close Firefox and are the backups in the sessionstore-backups folder present?

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)

Create a new profile as a test to check if your current profile is causing the problem.

See "Creating a profile":

• https://support.mozilla.org/kb/profile-manager-create-and-remove-firefox-profiles
• http://kb.mozillazine.org/Standard_diagnostic_-_Firefox#Profile_issues

If the new profile works then you can transfer files from a previously used profile to the new profile, but be cautious not to copy corrupted files to avoid carrying over problems.

• http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Firefox

It does create the sessionstore.js and the sessionstore-backups files.

I created a new profile. Set it "Show windows and tabs from last time" and changed browser.cache.check_doc_frequency to 2, so it should always use the cache version. I then opened several tabs. A couple were ones that change fairly regularly. (news sites that post new stories.) I closed the browser and waited. Then opened the browser and it went and refreshed the tabs instead of using the cache. I could tell because a new story was showing that was not in the cached version. So the new profile didn't solve the issue.

It appears I was a bit hasty checking the new profile and it did actually fix the issue. I've copied over about 90% of the old profile while checking that the fix was still working. I have all the plugins, signons, config, even the session history. I did try to have a cleaner profile by leaving behind file that seem to no longer be used. So bookmark backup and other backup files stayed behind as well as what seemed to be obsolete extensions.

The new profile works, though carefully coping and checking that the copied files didn't cause the problem in the new profile is tedious.