Do you receive any other emails from server? e.g. subscriptions? Do they work? Just checking, because if you're not receiving them, it may be SMTP setting.
We actually just fixed this issue and the Tableau server has been reconfigured for the email notification and restarted. I received notification the server had restarted. So what do you suspect is the problem?
As long as your Tableau Server is setup properly and tested (important point), then you should be getting alerts. There are settings the administrator sets up for alerts and perhaps they have not configured it for your Site or tested email notification. You might want to start a Tableau Support ticket if all that has been checked.