I have a user who used to be able to access our customer portal and no longer is. When I log in as her and click the project icon where most users are directed to the portal, she is directed to the project and sees the error 'This project isn't available'.
When linked directly to the portal she sees this:

Our customer permissions are set to 'Anyone with an account in <our_domain>', and when I look up her account in the Permissions Helper, it shows that she has permissions to create issues.