Skype says it's a software issue that they are working on. For me, it's six hours now and I haven't had more than a few minutes of "connectivity" in the past hour. And, when connected, the on-line count was at a new low:
Another glance through DESCLAUX and KORTCHINSKY part 2 suggests, in addition to traffic from clients to login servers, Skype generates a lot of traffic between the login servers and supernodes (see slide 16 for example). This makes the login servers a doubly critical piece of Skype infrastructure. Of course, if they merely introduced a bug in their login servers, it shouldn't take 12-24 hours to do a roll back.