I am having this same problem also.
On a Windows server running IIS, a web site can be set up for Windows Authentication.
On sites where we use Windows Authentication (which includes intranet web apps and SharePoint), it accepts the login but the page never loads. The spinner at the top continually spins, and nothing ever displays in the Safari window.
When using Chrome on the same device, it works.
And this worked with Safari on iOS 6, just prior to upgrading the device. Safari on iOS 7 breaks it big time.
BTW, this was on my iPhone 4S 32GB.