Sorry my ignorance in this...I was having the same problem as stated above. I have found that the blog I am trying to back up is apache...but I am not sure what to do with that information.

Can you explain a little more?
Thanks!

The "ownership restrictions" restrictions part means that the owner of the backup directory needs to be whatever user PHP is running under. (Just being writable by everyone--the 777 part--isn't good enough).

If you look at your files using your FTP application, you'll notice the ones you uploaded are owned by your user account on your host. But you should see some files owned by another user account that PHP runs under--often it's named "apache" or "www." The surest way to find out is to ask your host.

I'm sure this is a very simple fix, but I could not find exactly where on here the info was to fix this problem. I am getting this error message on my backup settings page:

WARNING: Your backup directory is NOT writable!

WARNING: Your backup directory is NOT writable! We cannot create the backup files.

This problem seems to be caused by your server’s safe_mode file ownership restrictions, which limit what files web applications like WordPress can create.
You can try to correct this problem by using your FTP client to delete and then re-create the backup directory: (my directory here)

I checked the folder wp-content and it's file permissions are set to 777. I also manually added the folder in there and it still would not accept it. Any help would b egreat!