Difficulties with Secure Mail Key

I routinely use Thunderbird to manage my email.  Once in a while I sign on to the ATT Web Mail site to be sure discarded email messages have been actually deleted.  I'm using a secure mail key, both in Thunderbird and for access to the ATT Web Mail.  Today the secure mail key no longer works when I go directly to the ATT Web Mail site; however, it still works fine when I access my mail through Thunderbird.

What is happening?  I'm finding the secure mail key process to be quite confusing, especially with statements in your instructions that say,  something like, "You can use your regular email password until a new secure mail key can be created."  Doesn't a new secure mail key BECOME the new password?  What's the point of ATT allowing me to create a secure mail key as a password instead of my creating my own password like I do everywhere else on the internet???