IE 11 first-party session cookies being lost in iframe

Question

We have a site (www.example.com) which sends users off to a series of third party pages to verify payment details, which we do in an iframe. Initially, a local page from www

Answer 1

I have noticed session cookies are often lost when IE7 compatibility mode is engaged for a new page. I suppose the same could apply to the iframe. Is the iframe sending a X-UA-Compatible header value that is different than the parent page, or different than earlier in the session? Like maybe your session started with IE=edge, and the iframe page sets it to IE=7. If so, IE seems to spin up a new IE PID for the compatibility mode pages and session cookies often (but it seems don't get transferred.