Profile data can be removed or not recorded in several ways;

• 1) Running Firefox in Private Mode (nothing is recorded)
• 2) Privacy settings; (In the address bar,type about:preferences#privacy<enter>)
• 3) Many disk cleaners and anti-virus type programs can remove data from browsers.Open their settings and have them leave the browsers alone.
• 4) Mal-ware.

Your ‘logged-in’ status is stored in special cookies. If the cookie is removed, you are logged out.

You may be in Private Browsing mode or told Firefox not to remember.

Type about:preferences#privacy<enter> in the address bar. The button next to History, select Use Custom Settings.

Turn off Always Use Private Browsing Mode Turn on Remember My Browsing And Download History At the bottom of the page, turn on Clear History When Firefox Closes. At the far right, press the Settings button. Turn on ONLY Cache and Form And Search History leaving the others off. and whatever else you want.

Thanks for the note, I tried it but unfortunately the issue still persists

Go to your Google profile page. Check its settings. Select Keep Me Logged In

Yes, all of this is turned on.

Let the cookies expire when Firefox is closed to make them session cookies instead of using "Clear history when Firefox closes" to clear all cookies including cookies with an allow exception you may want to keep.

• Options/Preferences -> Privacy & Security
  Cookies and Site Data: [ ] "Delete cookies and site data when Firefox is closed"

You can create a cookie allow exception with the proper protocol and use "Delete cookies and site data when Firefox is closed" to let cookies without allow exception expire when Firefox is closed.

• clearing "Site Preferences" clears exceptions for cookies, images, pop-up windows, and software installation and exception for password and other website specific data
• clearing "Cookies" will remove all selected cookies including cookies with an allow exception you may want to keep