My installation has been stable for 24hrs so I am marking as solved.
I migrated from 32bit to 64bit (NE 6.0.6) using the Zimbra doc "Network Edition: Moving from 32-bit to 64-bit Server "
Modifications to instructions in the doc:
1) Doc states zimbra_logger_mysql_password and mailboxd_keystore_base_password be modified in localconfig.xml. Don't worry if you can't find these - they are not present in NE 6.0.6
2) If you are not using a commercial SSL certificate, then DO NOT change the password (value) for mailboxd_keystore_password in localconfig.xml
3) If you find that the stats process stops, as root change permissions with
chown zimbra:zimbra /opt/zimbra/zmstat -R