This is a known bug in Magento's Cron Job system but it has not been resolved to date and it can seriously hamper website operations especially when Magento 1.9.x now requires the Cron Job to send out emails.
If you have ruled out all other issues with the Cron Job, follow the steps below to fix this bug for your Magento store.
Open up the cron.php file in your Magento root directory (usually "public_html") and look for the following line of codes:-
$isShellDisabled = (stripos(PHP_OS, ‘win’) === false) ? $isShellDisabled : true;
Add the following codes in a new line exactly after the above line of codes:-
$isShellDisabled = true;
SUPEE-6788 and Magento Community Edition 18.104.22.168
If your Magento store is patched with the SUPEE-6799 security patch or upgraded to Magento Community Edition 22.214.171.124, you will need to make sure that your Cron Job is configured not to use CURL or WGET but instead execute by PHP instead:-
/usr/local/bin/php -f /home/<cPanelUsername>/public_html/cron.php