Yes, that isn't a permission problem. I deleted all files from /var/log/httpd. The files are created, but all $domain.bytes files are always empty.
Today I found another problem. In every VH is line:
php_admin_value sendmail_path '/usr/sbin/sendmail -t -i -f |USER|@|DOMAIN|'
It sets the sendmail_path to '/usr/sbin/sendmail -t -i -f |USER|@|DOMAIN|' and in that case the mail() function in PHP doesn't work. It should be set to:
/usr/sbin/sendmail -t -i -f |USER|@|DOMAIN| (with out the ' ').