Could be you have corruption in your preference file. Shut down DEVONthink, move the preference file to the desktop, and restart. You’ll get default settings, but you can also test the backup preference to see if it works as expected. If so, then check with Support about the possibility of repairing the pref file.
Bill De Ville posted a good article about backup here:
Bill recommends using the File > Export > Database Archive … regularly. Over here, I don’t do that because it means I have to remember to do it. Instead, I clone my laptop (including DEVONthink databases of course) each day – two clones to two external drives. Carbon Copy Cloner does this automatically for me, so it’s not a big deal. I also have two Time Machines and 24x7 backup running to CrashPlan. All these also are automatic, reliable, and no fuss. (I plan to get rid of Carbon Copy Cloner because they eliminated a feature that we could buy a replacement hard drive with all archives on it – without that, any significant restoration from Carbon Copy would be prohibitively time consuming.)
I’ve restored databases a few times from Time Machine. Short of failure to open, there is no way simple way of knowing if the database integrity is 100%. That’s why I clone, and probably why Bill Archives.
Joe Kissel’s book on backup methods (recently updated) from Take Control Books is a great source.