Are you using Thunderbird Junk controls? Do you have Junk Controls turned on in Account Settings? If so what action do you have setup? Mark as Junk and leave in the Inbox or mark as junk and move to a new folder?

I have junkmail controls turned on and the messages, when first marked as junkmail, are filtered to the Bulk Mail folder.

From the bulk mail folder, I un-mark the messages, either by toggling the junkmail flag or opening the message and clicking on the Not Junkmail tab. When I do that, the message ends up in the correct folder, but is re-marked as junkmail.

If I un-mark the message in the correct folder, it will either be re-marked as junkmail within seconds (I see it happen) or if I scroll through the messages in the folder, when I go back the just un-marked messages, they're re-marked.

Thunderbird does not use a bulk mail folder. Yahoo does. Is Yahoo your email provider? Turn junk controls off in Thunderbird. Do the messages still get moved? If so, look elsewhere.

att.net IMAP has the Bulk mailfolder.

The problem is not the movement of the messages.

The problem is that I cannot un-mark them as junkmail.

AAT used mail services provided to them under contract by Yahoo. So YAhoo was the service that I could log into my yahoo account using the ATT web mail link on their web site. I was of the understanding that they had moved on to a somewhat more successful partner as the Yahoo service simply was appalling. If I recall correctly those that chose to stay with the Yahoo service could. Perhaps you are one who chose to stay.

Regardless, the product that uses Bulk mail as a folder name is YAHOO. no other provider uses that folder name for spam. SO you are using yahoo!, even if it is being sold to you as something else.

Yahoo do not offer a opt out for their silly spam filtering, apparently they know better than their users. They also appear to scan all folders over and over and mark any mail that has been marked as not junk as junk again because their algorithm says it is. As IMAP is synchronized whatever happens on the mail server is faithfully synchronized to Thunderbird.

The short of it is get another provider, one that does not run roughshod over your decisions. Vote with your feet.

GMX, Gmail, even AOL are all better than the Yahoo offering. Although I fear for AOL now they are owned by the same company as Yahoo. But there is nothing Thunderbird can do to stop Yahoo "fixing" your spam.