Hi,
There are two things to check. The first one is the Queue Process in your Acymailing configuration. Make sure that the queue processing option is set to one of the automatic options.
The second thing you need to check is the automated tasks setting on the License tab of your Acymailing configuration. Normally this should be activated. But if you created a cron job on your own server it shopuld be deactivated in order to prevent two cron server trying to trigger your automated tasks.