You can create a cookie exception via "Settings -> Privacy & Security"

• Settings -> Privacy & Security
  Cookies and Site Data: "Exceptctions"

Make sure you use "Delete cookies and site data when Firefox is closed"to clear cookies that do not have an allow exception and not "Clear history when Firefox closes" as the latter removes all the cookies including cookies with an allow exception. Also make sure you keep the Site Preferences as that includes removing all the exceptions.

Thanks. That's what I was doing, but I guess Google webmail is just a POS. It works fine with keeping me logged-in to my Yahoo webmail.

For Google websites you can create the exception for "https://google.com".

Thanks, I really appreciate your assistance. I tried exceptions for https://google.com, https://mail.google.com, https://calendar.google.com -- none of these work for keeping me logged into my google account between sessions. POS google requires me to have my mobile phone next to me to log back into my account. All-knowing and all-powerful arrogant google, if it weren't for my company's choice to use google I would dump them in a heart beat.

Many days later (and several reboots later, but no software updates or configuration changes), it has magically started working with my google account. I am unable to explain how it worked for all my other web logins immediately but apparently google just needed to think about it for a while.