For some reason I was under the assumption that Thunderbird stored a copy of each message in subscribed IMAP mailboxes. As it turned out, this assumption was 100% incorrect with the default settings, and so a large chunk of email archives that I thought I had stored from 2004 and 2005 are now gone. Darn.
It is possible, however, to enable this life-saving feature. What you have to do is go to your account settings (Tools menu, select Accounts), then on one of your IMAP accounts go to the Offline & Disk Space section. On this page make sure to check the two top options (Make the messages in my inbox available when I am working offline and When I create new folders, select them for offline use), then click Select folders for offline use, and in the window that pops up go through the list checking off all of your important folders (usually everything except for your Trash and Junk mailboxes).
That turns on the feature, but it won't automatically cache all of the email that has already been listed. To do this you simply go to the File menu in the main program, select Offline and then Download/Sync now. The window that pops up lets you select what you want to download (email, news or both), then just click OK to have Thunderbird fly through your email and download it all.
While I'm not sure why this extra level of caching is not turned on by default, a little bit of fiddling to get it working will ensure that you don't end up loosing two years of email.