Magento 1.8 – How to Fix Missing Sitemap.xml

A Cron Job with no finished_at time, it probably never finished.

You should find something in your error logs.

Also it helps to use the module http://www.magentocommerce.com/magento-connect/aoe-scheduler.html to debug, as it allows to call your cron directly from cli via:
php shell/scheduler.php -action runNow -code productimporter_import_xml

As you mentioned you have setup Magento in new VPS server.

so maybe you missed to set up cron in crontab please check crontab -l from root directory via ssh.

Did you see cron setup there? if not then please use crontab -e to setup cron in crontab and paste below code there.

#~ MAGENTO START
* * * * * /usr/bin/php /var/www/html/magento2/bin/magento cron:run | grep -v Ran jobs by schedule >> /var/www/html/magento2/var/log/magento.cron.log
* * * * * /usr/bin/php /var/www/html/magento2/update/cron.php >> /var/www/html/magento2/var/log/update.cron.log
* * * * * /usr/bin/php /var/www/html/magento2/bin/magento setup:cron:run >> /var/www/html/magento2/var/log/setup.cron.log
#~ MAGENTO END

for more details follow below link

https://devdocs.magento.com/guides/v2.2/config-guide/cli/config-cli-subcommands-cron.html

I think you should install free magento2 extension to check your cron status if not installed where you can track your cron

https://www.wyomind.com/cron-scheduler-magento.html