It looks like there is no activity on the Kentico admin side. The emails from the Email Queue are sent by a scheduled task. And the scheduler is running only when the Kentico application is up and running and, by default, there has to be some request made - the default scheduler is request based (for more details please see the documentation). Or, you can use the Automatic scheduler mode, but the Kentico application must be alive (always on).
Task execution by the Kentico application runs within the ASP.NET process, so tasks cannot be executed if the web application is not running. The application stops running when the process is recycled without being started again (after a long period of website inactivity).
If you want to run the scheduling reliably, we recommend using the Windows scheduling service. EMS license required.
To achieve reliable task execution without using the Windows scheduling service, you need to ensure that your website is always running. For example, you can prepare a utility or service that requests the home of your website on a regular basis.