Hello, I have noticed several problems with this plugin:
1) Is described in another support ticked:
2) It looks like that everything works fine when the W3 Total cache is disabled. Today february 1 I had in the options "Next backup date: 28 january 2013 @ 12:22". However after many tries to disable the plugin because of the problem number 1, as soon as (1 minute after) I got it disabled, the backup with WP-DBManager has been done and sent to my mail.
3) When W3 Total Cache is enabled the number (white digit in a black cicle) of plugins to update doesn't appear in the left sidebar of the admin-cp. As soon as I disable this plugin, the number of plugins for which there is an update available appears.
I started having these problems in January.
I hope you can help