Do you have any product on your computer like CCleaner or perhaps an Anti-Virus product with cleanup abilities because they might be killing the saved passwords or the session files?

If yes, then you need to stop allowing the cleaning product from access to Thunderbird.

There is "Bitdefender" and "Driver Support" in the background, but they never made a problem. The problem started just after the new version of Thunderbird was installed. I deleted the email accounts and add them again, but the problem is still the same.

Bitdefender has a password manager (Wallet). Check that it's not storing TB passwords. If that's not a factor, Help/Troubleshooting, Profile Folder, Open Folder, close TB, delete or rename cert9.db, key4.db and logins.json. This will erase all passwords, but when you restart TB and enter the passwords, they should be stored permanently.

http://kb.mozillazine.org/Password_not_remembered_-_Thunderbird

Thank you, great support. It works perfectly now after deleting this 3 files.