The link Clay provided didn't have any info. that even came close to my question.
I only use Outlook for work, otherwise, I'm not a MSFT user at all.... I'm an Apple user. Furthermore, I'm just an office grunt, not a dev. or anything... example - I have no idea what a federated tenant is, or most of the stuff on the link Clay provided.
So after seeing your answer (thank you - it came as close to helping me as I've gotten so far), I figured I'd first test out the theory using the Incognito mode on Chrome (again, no Explorer... I'm on a Mac, so I can't use Explorer, but wouldn't even if
I could).
It worked! Well... let's just say that I at least got as far as getting back the pop up that gives me the option to stay signed in. So I signed out on my Incognito mode, closed that browser instance, went back into regular Chrome, and cleared out all the
cookies related to anything MSFT (Outlook, Office, etc.).
After I did that, I was able to (finally!) get the "Do you want to stay signed in?" prompt to come up. So I very happily clicked on the "Yes" (or whatever the affirmative box is), confident that THIS time, I wouldn't get automatically booted. I even played
it safe and made sure to NOT click on the "Don't show this option again" box... just in case it didn't keep me signed in, I figured by NOT clicking the "Don't show this option again", at least I'd get the option to stay signed in the next time.
Unfortunately though, a few hours later, I got booted again. And worse yet, the option to "Keep me signed in" did not show up. So I'm right back to square one again.
I'm back to getting booted at the worst times... the middle of conference calls when I'm having to reference emails, or pull up attachments to emails, etc... and NO warning! NO countdown option to just click a box to stay signed in "or else"... nothing...
boom! "Please wait while we sign you out of Microsoft Outlook".
And THIS is exactly the kind of stuff that caused me to jump ship from all things MSFT in 2009 and never go back until forced to do so by my job. But again, thank you anyway. I really appreciate your desire to help. And like I said, I got as close to it
working as I've come so far.