I've got different version of zimbra (8.0.4), but I was fighting with simmilar issue. It may help someone.
The call to /opt/zimbra/libexec/zmlogprocess wasn't in his place in crontab.
Execute as zimbra user following command:
If it gives you empty result, add to zimbra user crontab content of file /opt/zimbra/zimbramon/crontabs/crontab.logger
$ crontab -l | grep zmlogproces
You may try run the script /opt/zimbra/libexec/zmlogprocess by yourself. After that command
shouldn't gives you errors.
/opt/zimbra/libexec/zmrrdfetch -f zmmtastats
I've found this solution on Fix Zimbra stats graph/cron jobs | Platonic