The battery saving tools are killing the background process and Notifications are not being pushed to the watch anymore.
There is an option to exclude the Android battery saving mode:
Settings -> Apps & Notifications -> Apps -> Settings (Icon below) -> Special access -> Ignore Battery optimization -> Change "Allowed" to "All" to see Connect Mobile -> Tap & change
which not entirely work for Huawai devices.
But there is another thing, you can do! You can "Lock" the app from being killed in the Task-view:
This helped me and the Notifications are being pushed since a whole day without opening Connect Mobile manually.