Also same issue since 24th September.
Application: ASP.Net Web Forms (HTTP:80 only)
Server: Windows Server 2012 (Windows Azure Virtual Machine)
Authorizer: WebAuthorizer with InMemoryCredentials
I noticed that this issue happens 25% of the time, but when the issue happens, if you refresh the page and try again, it keeps happening.
My application is not using SSL, all my requests are HTTP.
I found this article on the Twitter blog:
Streaming SSL certificate updates
As I understand this change only applies to exisitng applications using SSL, so that shouldn't be the cause of the problem.