Why is this suddenly happening in Thunderbird??

Can you click on the "View" button from the first screenshot and post what that says? That should should give some clue on the nature of the invalid information mentioned in the error. 

Hi Tiffany, yes it works on pop.cox.net. I wonder how long ago that changed, if it just changed, or what. Because like I said I've been using it for years without any issue at all. Still indicates that the cert on your server changed somehow. But all is good now, thanks.