How to properly work with the auth.logout method?

Question

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I hang a handler on the authorization and deauthorization event
as:

VK.Observer.subscribe("auth.login", function f()
{
alert ("Thank you for your Login.");
});

VK.Observer.subscribe("auth.logout", function f()
{
alert ("Thank you for your Exit");
});

The login event fires when you successfully log in for the FIRST time, then I press the exit button, the logout event does not fire !!, I log in again and unfortunately the handler for the login event does not work ...
Please help solve the problem, otherwise it is not clear whether the user registered on the site or No...