Hi Marko welcome to the community.
If you use multiple devices, it makes sense to enable “send copy to yourself” everywhere, so you see your own messages on all devices: https://delta.chat/en/help#what-is-the-send-copy-to-self-setting-good-for
iOS often stops Delta Chat from running in the background, and only wakes it up occassionally. Note that Delta Chat doesn’t use Google Cloud Messaging (GCM) or the Apple Push Notification Service (APNS), because this leads to user tracking and central control which Delta Chat aims to avoid as much as feasible.
However, that Android and iOS kill apps running in the background is a problem for many legitimate apps. For more information, see dontkillmyapp.com.