Filters work on Inboxes and respond to incoming mail. As you have described it, using filters to move messages to Local Folders' Inbox, I wouldn't expect filters in your Local Folders Inbox to run automatically, since it isn't a genuine Inbox. I do the same myself; an IMAP-connected account has copies made to Local Folders (by filters) to guarantee I have a permanent copy of correspondence even when off-line. But the filters set up for Local Folders don't fire on these moved/copied messages.

So, why does it offer filters on the Local Folders Inbox? If you were using POP and had set it to use the Local Folders/Global Inbox, then the Local Folders Inbox would be serving as the Inbox for those POP-based accounts and it would indeed run its filters on receipt.

I use a Run Filters button on the Toolbar to make my filters work in folders other than the accounts' own Inboxes.

You mentioned that all of these filters used to work fine when you first set them up. I've experienced what seems to bee the same problem on my computer, and hopefully, the solution I found will work for you, as well.

What happened on my computer was that my index files (.msf files) had gotten corrupted. If the index files have gotten corrupted, the filters won't be able to move the mail into their assigned target folders because the folders don't appear to exist to the filter any longer.

You can simply highlight the target folder (in this case your target Inbox), and wait for the index to rebuild (a progress bar will appear on the bottom of the screen), or you can force the application to build a new .msf file by going into your application data/Thunderbird/Profiles/Mail/<account name> folder and delete the target folder's .msf file. Then when you highlight the folder in Thunderbird, it will index and rebuild a new .msf file.

It took me a couple of hours to figure out why my message filters had suddenly stopped working, as I had quite a few emails set up to go right into the "trash" folder. Ordinarily, I don't go into my trash folder, so like yourself, I found myself checking my filter configurations, and going around in circles with this. When it occurred to me that those .msf files do get corrupted on occasion, I simply highlighted the "trash folder", the contents were not visible at first as the index rebuilt itself, and once the index was working properly again and the contents of the folder were again visible, the filters all began working properly again.

Hope this does the trick for you...!