It is across all ASP.NET applications, meaning that when it happens, none of the other ASP.NET apps is responding (they behave just like the requests are not relayed to the apps anymore). And it is intermittent, which makes this a tough one.. It happens every few days, sometimes once a week.
One more detail, which seems to be common to all situations: the failure never occurs while you are in the application. Only when you open the browser, type in the address, hit enter, and expect to see the login page...