Are you using these filters in Thunderbird or server side? Thunderbird filters generally only run on the inbox and sent folders, and then only on new items.

Are the affected messages Spam/Junk? Some providers, Yahoo/AOL/ATT being one ignore our choices and force their determinations as to what is junk/spam on you. In their view you are apparently not in change as they offer no way to opt out of their filtering.

This is a Thunderbird message filter. It's set to apply when Manually Run, and when Getting New Mail.

When I disable the filter, it stays where I put it. When the filter is reenabled, it still stays there.

It also stays there if the filter is enabled but Thunderbird is offline. When I take it back online, the message moves back.

So whatever is triggering the application of the filter to the message, it happens when a new message is moved to the folder and TB is online. If the filter is enabled after those conditions have happened, the filter is not reapplied to the message.

Edit: It's not likely to be the server because I'm moving the message from the inbox where it was originally sent to the inbox of another account on another server.

Personally I think what you are doing is asking for trouble. Silent failures in this sort of action are not really all that uncommon. Having stuff move back from whence it came is perhaps one of the signs that silent sync failures are occurring.

It does sort of work, most of the time. Generally it is slow and there is no feedback as to when the process is completed. It might be many minutes after you see things zip around on screen for the actual process to complete. It should not be attempted while offline at all as the entire process requires multiple round trips to both servers. It is certainly not a function I would encourage doing with a filter, as the filter will just kick off the process and not wait for any confirmation of the completion of the IMAP sync.