Automatic update of the Authentication Proxy isn’t available in the product today. Some customers use management frameworks like Chef, Puppet, Ansible, and others to automate updates.
The risk of automatic updates is that no user authentications or directory sync processes can happen during the upgrade install, so if you choose to deploy updates automatically be aware of temporary unavailability and schedule during maintenance windows or periods of low usage.
You can contact your Duo account executive or customer success manager to submit a feature request for built-in automatic update functionality. If you don’t have either of those contacts available, Duo Support can assist with submitting your feature request as well.