ResolutionStatistics in Plesk is counted by means of the /usr/local/psa/admin/sbin/statistics utility, which is run by cron every day.
In Plesk 8 and previous versions cron job for statistics is placed in the 'root' user crontab:
7 4 * * * /usr/local/psa/admin/sbin/statistics >/dev/null 2>&1
Since Plesk 8.1 it is located in /etc/cron.daily/50plesk-daily:
/usr/local/psa/admin/sbin/statistics >/dev/null 2>&1
So, make sure that statistics cron job exists and crond is running:
# ps -ax | grep crond | grep -v grep
and check cron logs (/var/log/cron) for records about the statistics utility executions.
Also, you can try to run the utility manually and look for errors. Make sure that there are no apache logs bigger than 2 GB. It may cause webalizer to fail.
Make sure that all database directories in $MYSQL_VAR_D (usually /var/lib/mysql) have read/write permissions to 'mysql' user.