Even though StillAlive has checked your site and found it to be down, there are two circumstances when it will still NOT send notification of failure nor log such failure in the "Notifications" page. These circumstances are both to do with how Still Alive has been (or not been) configured to send you notifications.
First of all you must have entered your email address (or SMS or Twitter details if you are using these paid services) in the Profile page.
Secondly, you must have at least one form of notification activated in your "Collaborators" page settings. To get to these settings first select and view your site from the dashboard and then select "Manage Collaborators".
Then check the appropriate selection(s):
It is a good idea to then select "Send Test Messages" to test that it is all working as desired.