For various reasons, subfolders can get into the “not to sync” state in thunderbird 3.x. This is rather annoying as you will miss quite a lot messages, if you are e.g. using sieve mail filters on the remote imap server.
to turn that on do the following:
Edit – Preferences – Advanced – Config Editor – I’ll be careful, i promise!
Then enter
mail.check_all_imap_folders_for_new
and set that to true (“Toggle”).