M. Tibbits answer alludes to allowing Piwik to use more resources during the archiving process.
After testing this, it appears there is a limitation on how large an SQL command can be executed, which defaults to just 1MB. For more info; Packet too large
To increase the size limitation in MySQL, edit /etc/my.cnf and set max_allowed_packet=32M
Ensure the PHP memory limit is set to be high enough per forked process by editing /usr/local/lib/php.ini and set memory_limit = 512M
Finally, ensure all processes have at least a 1G hard limit before the system shuts them off by executing ulimit -v 1048576 on the command line.
Update
ulimit -v 1048576 will only raise the soft limit. If the hard limit is not high enough, the system will automatically reset the soft limit to that of the hard limit.
To set the hard limit, add the -H switch:
ulimit -vH 1048576