The server doesn't send out an alert when it goes down
As Toby says, no alerts are sent while server is down. However, there are solutions out there for external monitoring to go and ping your Tableau Server and if the expected response is not returned, then alerts can be sent via the external monitoring. One such example can be found here: Enterprise automated monitoring
You may want to use third-party tools which ping your server URL every few minutes if you get 404, tools will send you a notification email.
PHP Server Monitor