Hi Rob
Wondered if you'd got an update to this problem....I'm experiencing exactly the same thing. Most of our users have been able to login using SAML authentication since upgrading to Notes 9. But a few (consistently) can't. They login, get the prompt that the ID file is being downloaded etc and then next time they login, they have to select their ID file.
What's particularly odd is that we are running Citrix installs of Notes, and in theory every user should running in the same environment. Why it's working for some but not others is a mystery at the moment. Tried re-creating a user, same result for that user. We have the root certifier in our policy as well as the cross-certified ADFS cert. It must be correct because, like I say, most users are functioning correctly. If you could update with anything else you found I'd be very grateful. Thanks.