The data source connection for a feature service that is added to ArcMap is broken. The feature service is visible in ArcCatalog, but when attempting to repair the connection to the data source via the Layer Properties dialog box, Properties > Source tab > Set Data Source > My Hosted Services, the path to the feature service cannot be found.
The feature service may have a broken data link if the data source that it references has been moved, renamed, deleted, or is inaccessible. Feature services that are added to ArcMap use their REST page URL as the data source link. The Set Data Source button is only for feature classes and not for feature services.