Security roles are not correctly applied, causing access issues.

I am having an issue where security roles are not being correctly applied to users, causing access issues.  
When a user is assigned a role, they are not able to access the resources that the role should grant them access to.  I have checked the role assignments and they are correct.  I have also checked the user's permissions and they are correct.  I am not sure what else to check.  

Has anyone else experienced this issue?  If so, how did you resolve it?V