A common issue I've seen recently is where Magento cron jobs aren't being executed successfully (so transactional emails don't get sent and so on). The cron job executes when you run it from the command prompt, but not when you run it via the cron.
The fix is to edit the Magento public_html/cron.php file, and find these lines:-
$isShellDisabled = is_array($disabledFuncs) ? in_array('shell_exec', $disabledFuncs) : true;
$isShellDisabled = (stripos(PHP_OS, 'win') === false) ? $isShellDisabled : true;
And then add this line immediately below those to read:-
$isShellDisabled = true;
When you now execute the cron job, e.g.
It should now execute successfully.
To monitor whether the cron is working successfully or not, there is a very good module called AOE Scheduler which you can get here:-