RESOLUTION
If you get the following error when try to run 'statistics' utility:
# /usr/local/psa/admin/sbin/statistics --calculate-all
Webalizer V2.01-10 (Linux 2.6.9-34.0.2.ELsmp) English
Using logfile STDIN (clf)
DNS Lookup (15): db_put fail!
It means that /usr/local/psa/var/lib/webalizer/webalizer.cache or /var/lib/webalizer/dns_cache.db files were damaged or exceeded 2GB. These files are used by 'webalizer' to cache DNS queries when it resolves IPs from access_log requests to Apache came from. Remove the file and run 'statistics' again.
If you don't need to resolve IPs or statistics you can disable it by commenting DNSCache and DNSChildren directives in /etc/webalizer.conf and /var/www/vhosts/DOMAIN.TLD/conf/webalizer.conf files.