There is an enhancement bug open for that. https://bugzilla.mozilla.org/show_bug.cgi?id=446444

I think Comment 36 basically translate to it's not going to happen.

Alexandre.Rodrigues said

Please. Make the difference. Put the sync firefox feature on the thunderbird and make your email client most usefully If you lose messages filters you will have a big problem

Still not backup all my filters

re: Still not backup all my filters

If you backup your Profile, the this will backup all mail accounts, emails, preferences, address books, Message Filters etc etc etc.

• http://kb.mozillazine.org/Profile_backup
• http://kb.mozillazine.org/Profile_folder_-_Thunderbird
• http://kb.mozillazine.org/Keep_it_working_-_Thunderbird

You can also backup Address Books independently: In Address Book

• select address book
• Tools > Export
• select either LDIF or comma separated .csv
• save to a folder outside of thunderbird.