Why not just do a once-a-day backup to your local disk? Throw out the old ones once a month or so. Unless you've got a big database, that's less space than the application binary occupies.
You can control the warnings about stale sync clients with the techniques in Ken's post
here.
The only way you should be getting multiple warnings a day from one machine is if you have it set to back up multiple times a day, and/or have changed the sync parameters mentioned in Ken's post. If you don't care enough about your data to back up to an ever-present drive, why all the backup attempts?