I suggest adding some test logic in your LoginSamlPost method to confirm the customerId isn’t null.
If that looks ok, it’s possible the SAML session state, which is where the configuration name is saved, is being lost. This state is indexed by a saml-session cookie which is marked as Secure and SameSite=None. It’s possible this cookie isn’t being sent by the browser under certain conditions. This can be investigated using the browser developer tools.
It’s interesting that recycling the app pool resolves the issue.
If the issue can be reproduced easily, I suggest enabling SAML trace and sending the log file, along with a reference to your forum post, to support@componentspace.com.