Indeed, you can't append network features to the open diagrams in the following situations:
There are unsaved edits
The All Layers mode is not turned on on the diagram map to which you want to append new network features
This diagram is based on a template that doesn’t allows to extend diagrams
The diagram is historical and is considered as read-only
Another limitation is when working with a database connection to a utility network in an enterprise geodatabase; the Append to Diagram command only applies to a network diagram layer that is from either a network in a file geodatabase or a utility network service.
You must make sure that you are out of all these situations