Assigning SSO profiles to different Portal Access items on a full Webtop

I have. If the problem profile is assigned as the default, that app works. Any single profile can be assigned as default, and the app expecting that SSO profile does SSO correctly. But the SSO profile specified in the resource is never used, as indicated by the debug comparisons of URIs that only exist on the default profile. So, I have concluded that the resource assignment SSO profile is not taking effect for some reason.