That's a bear. Thanks for getting it back online.
If the site is hosted on a virtual private server and runs off mysql, you could easily write a batch file or bash script that is scheduled to run daily. This would issue a mysqldump command to dump to a directory on another machine (or external disk, depending on hosting environment). Alternately, if the database is sufficiently small, someone's home machine could make the connection and run the dump to the home machine (or just dump new records, though a restore becomes more complex).
I've seen this used on a small database before to backup across a local network. Depending on the database size/type and environment, this could be an easy and free option.