Could you check whether the sites' cookies still exist when you start Firefox? You can view them here:

orange Firefox button (or Tools menu) > Options > Privacy tab > "Show Cookies" button
(Note: this is only visible if you have selected for Firefox to "Use custom settings for history")

The dialog should show all the sites that have active cookies (cookies set only for the previous session would have been removed). Typically you will have many persistent cookies. If you have very few, it could indicate that your cookies are being cleared at shutdown.

There is a feature toward the bottom of the privacy tab to "Clear history when Firefox closes" but this feature uses history in a broad sense so if you are using it, click the Settings button to make sure you aren't clearing cookies there.

If Firefox isn't clearing the cookies, an add-on or external program might be involved.

Websites remembering you and automatically log you in is stored in a cookie.

• Create an Allow cookie exception to keep such a cookie, especially for secure websites and if cookies expire when Firefox is closed.
• Tools > Options > Privacy > Cookies: Exceptions

In case you are using "Clear history when Firefox closes":

• do not clear the Cookies
• do not clear the Site Preferences

• Tools > Options > Privacy > Firefox will: "Use custom settings for history": [X] "Clear history when Firefox closes" > Settings
• https://support.mozilla.org/kb/Clear+Recent+History

Note that clearing "Site Preferences" clears all exceptions for cookies, images, pop-up windows, software installation, and passwords.

Clearing cookies will remove all specified (selected) cookies including cookies with an allow exception.