We've searched quite a bit about this problem and it seems that the issue has been brought up before on other sites, but none of them really answered. We have checked this page.
M2E Cron jobs not automatically running in Magento
But our cron.php is successfully running and executing other scheduled tasks. According to AOE_Scheduler, the M2ePro_cron method is being scheduled and executed, but we still receive the warnings saying
Attention! The Cron job is not running at the moment.
And
Attention! Last eBay AUTOMATIC synchronization was performed by cron more than 12 hours ago.
The Cron Info section of the extension shows:
Last Run: 2013-06-08 11:02:43 (not working)
But I've set the cron.php to create a log of its run times, so I know it is still being executed. On top of that, everything else seems to still be updating correctly.
-Paul
After a few emails to M2e support, we were able to solve the problem. We had to remove the file cron.lock from the var/M2ePro folder. They said that this file is normally removed automatically and is used to prevent M2e's cron task from running more than once at certain time periods.
After removing the file, our M2e cron was running fine and updating automatically again.
Hope this helps the other people out there who have the same problem!
-Paul