I dont know of a service, but you could always use rsync from mac/linux or deltaCopy for windows to do a daily sync of the website to a local computer. schedule it for lunch time to ensure the computer is on everyday. A sync will be faster as it will only copy down what is different.
Hope that helps
Thanks for the thoughts.
I know that apps can be set up to mirror a site to a client computer...though the thought of a command line linux backup app gives me hives. I was kind of thinking that a turnkey solution from some 3rd party could be easy if priced right. My main objective: I don't want something where the client might look to me for support. I'd prefer to hand all that responsibility off.
How have others skinned this cat?
If you go with a host that offers Plesk you can use the Plesk backup feature which includes a scheduler. This feature backs up everything with one click - including settings & setup, mail, database (if you're using MySql) and files. If needed you can even switch servers by downloading the back up file, uploading it to another server running the same version of Plesk, hit restore and your up and running on your new server (after switching dns of course). This would be a good solutions for clients.
Can anyone recommend an inexpensive service that will back up a website on a schedule? I am looking for an alternative to telling clients to keep a computer running with FTP scheduled.