What version of PM? Enterprise? What operating system? Manual or Bitnami install?
Where those cases with the due date set to 1970-01-01 or created by or routed by a [urlhttps://wiki.processmaker.com/3.2/Executing_cron.php]cron script[/url]?
If so, then you may need to configure the date.time_zone setting in the php.ini
file used by the PHP CLI. For example, on my Debian machine, I have to configure /etc/php/5.6/apache2/php.ini for PHP executed by the web interface and /etc/php/5.6/cli/php.ini for PHP executed by the command line (which is what cron.php uses).
There is a function used by PM to calculate the due date. You might need to configure a calendar to get it to work correctly.
IN your env.ini
Do you see any error messages?