Have you checked Keepme logged in durin signing in to the websites.

To give you further assistance please give the website you are trying to login.

Yes, I have.

Thank you for installing the extension to gather your settings data. It shows this:

browser.privatebrowsing.autostart: True

In the Options dialog, if you set Firefox to "Never remember history" then every session is a private session with no cookies saved. Surprised? Firefox uses the term history very broadly in this dialog to cover nearly all personal data.

To switch off permanent private browsing:

orange Firefox button (or Tools menu) > Options > Privacy

Change Firefox will to "Use custom settings for history", then you can access the specific checkboxes, including unchecking the one for automatic private browsing.

Does that work?

Note: Sometimes the preferences file (prefs.js) can become locked and your settings are not saved. In that case, you might need to manually change it from read only to read/write, or delete it and have Firefox use default settings. This article covers that and other possible related problems: How to fix preferences that won't save.

See also:

• https://support.mozilla.org/kb/Private+Browsing