BackWPup v3.0.6 is working on my WP 3.6-beta1 test site.
1. Using the settings discussed in the following thread - http://wordpress.org/support/topic/backwpup-not-working-after-upgrade - ie. PCLZip
2. PHPZip mode (auto) also working, but much slower - maybe the problems found with live sites are server config related (I have the same bug mentioned above with my live WP sites where scheduled backups fail)
Manual and scheduled file and database backups created successfully without throwing errors or restart messages.
Localhost setup (XAMPP v184.108.40.206.1.0):