You have several choices for a 'backup' server, you can use the
always_bcc option in Postfix, some form of archiving solution such as MailArchiva (there's a free version IIRC, you'l also find details of several other similar systems in some of the forum threads) or maybe the Legal Intercept feature of Zimbra (search the forums & wiki for that term).
Restoring mail into a rebuilt server is always going to be a manual process and losing a production server will almost always result in the loss of some email up-to your last backup. Take a look at some of the backup scripts in the forums (some of them also do individual mailboxes) and see if they can provide a better or more up to date backup than your current procedure.
I'd also suggest you throw some of the responsibility for mail backup onto the user, I haven't used Thunderbird in a long time but see if there's any archiving/backup feature that might be useful for the users. You should also take a look at what Zimbra Desktop has in terms of local mail storage and backup features that might help the users make a decision about their own backup strategy.