M2E Pro Cron Service is a predefined free service. To run synchronization tasks, it sends the requests to the Extension endpoint each minute. However, in some cases, these requests do not receive an answer. Thus, the synchronization cannot be run. You may see then that the ‘Last Run’ time of the synchronization process is colored in red under the eBay/Amazon/Walmart > Help Center.
The situation is mainly caused by the blocking of outgoing connection - the M2E Pro Servers (s1.m2epro.com and s2.m2epro.com) and Cron Service (cron1.m2epro.com and cron2.m2epro.com) must be in a list of allowed incoming/outgoing connections. So you should check if they are not blocked by your Firewall or by any other settings of your server.
Alternatively, you can set up Magento Cron. In this case, automatic synchronization will be performed based on Magento Cron job settings. This configuration can also be helpful in case the M2E Pro Cron Service execution temporarily fails. Since Magento Cron will trigger the tasks until M2E Pro Cron Service is restored. Check the instruction for Magento Cron set-up.