I have a web site that is trying to call an MVC controller action on another web site. These sites are both setup as relying party trusts in AD FS 2.0. Everything authentica
In the project which I currently work with, we had the same issue with SAML token expiration on the clientside and causing issues with ajax calls. In our particular case we needed all requests to be enqueud after the first 401 is encountered and after successful authentication all of them could be resent. The authentication uses the iframe solution suggested by Adam Mills, but also goes a little further in case user credentials need to be entered, which is done by displaying a dialog informing the user to login on an external view (since ADFS does not allow displaying login page in an iframe atleast not default configuration) during which waiting request are waiting to be finished but the user needs to login on from an external page. The waiting requests can also be rejected if user chooses to Cancel and in those cases jquery error will be called for each request.
Here's a link to a gist with the example code:
https://gist.github.com/kaveh82/bb0d8e4a446496a6c05a
Note my code is based on usage of jquery for handling all ajax request. If your ajax request are being handled by vanilla javascript, other libraries or frameworks then you can perhaps find some inspiration in this example. The usage of jquery ui is only because of the dialog and stands for a small portion of the code which could easly be swapped out.