Layer files created by right-clicking on a network analysis sub-layer (for example stops or routes) in the table of contents and then clicking on 'Save as Layer File' are disconnected from their feature class.
Network analysis layers (for example route, closest facility, or service area layers) hold an in-memory workspace containing the feature classes that the sub-layers are referencing. If the sub-layer is saved independently to a layer file, the workspace is not saved and so the layer loses the connection to its feature class.
Get help from ArcGIS experts
Download the Esri Support App