Does it have write access for /var/log/apache/ssl_mutex.1260 ?
For my server, Apache runs as user and group httpd. Here are the permissions for /var/log/apache:
$ ls -ld apache
drwxrwxr-x 4 root httpd 544 2006-08-22 10:56 apache/
What are your permissions and who does Apache run as?
EDIT: fixed to sound better