I get the same sort of behavior here. Tried completely uninstalling and then re-installing, but it does not resolve the issue.
Here is the output from the php error log:
[Tue Sep 16 00:31:14.656080 2014] [fcgid:warn] [pid 18725] [client 174.32.114.182:40397] mod_fcgid: stderr: PHP Fatal error: Cannot redeclare class UpdraftPlus_BinZip in /var/www/clients/client0/web1/web/wp-content/plugins/updraftplus/class-zip.php on line 12, referer: https://smallbeartechnologies.com/wp-admin/options-general.php?page=updraftplus&settings-updated=true
Running version 1.0.19 of the plugin on WP version 4.0