If you have correctly setup your authorized_keys and are sure it should allow you logins with keys – then maybe SELinux is giving you a hard time. Especially if your user is not under the normal home directory folder /home. In your /var/log/{auth,secure} files you will see that sshd is not allowed to open authorized_keys and/or authorized_keys2 after you set the “LogLevel DEBUG” in /etc/ssh/sshd_config.
In that case, try to set the correct settings again:
chcon -t ssh_home_t ~PROBLEMATIC_USER/.ssh/
chcon -t ssh_home_t ~PROBLEMATIC_USER/.ssh/authorized_keys
Now everything will work again.