I was getting the following error when using BackupBuddy on a VPS:

HTTP Loopback Connections are not enabled on this server. You may encounter stalled or significantly delayed backups.

The solution was to add the following to my vhosts.conf file on the server:

127.0.0.1 www.mydomain.com localhost localhost.localdomain
::1 www.mydomain.com localhost localhost.localdomain

For a detailed reasoning, check out this and this.