I keep getting an alert saying I need to update my email account.

Please post a screenshot. https://support.mozilla.org/kb/how-do-i-create-screenshot-my-problem

Here's the screen shot of the notice that keeps popping up (for months).

The screen shot you uploaded shows icon of Mail (of Microsoft), not Thunderbird.

No response yet.

Dear YU5. True, but sbcglobal is the part after the "@" symbol in my Thunderbird email addresses. My full Thunderbird would be like this: my name@sbcglobal.net

1.

Dear YU5. True, but sbcglobal is the part after the "@" symbol in my Thunderbird email addresses. My full Thunderbird would be like this: my name@sbcglobal.net

I am sorry that I do not understand what you mean. Thunderbird is just an email client, not an email service provider. Although Thunderbird can access emails from the address "my name@sbcglobal.net", Thunderbird does not own "sbcglobal.net".

2. What I mean in my previous reply is: that alert is generated by Mail (of Microsoft), not generated by Thunderbird. You should update you email account in Mail (of Microsoft), not in Thunderbird. And here is forum for Thunderbird, not forum for Mail (of Microsoft).