In some situations, you may have a web map with a bad feature service you are trying to edit or remove, but it has seemed to have disappeared, or you can no longer access the feature service in question.
When you open the web map that has the bad feature service, ESRI recommends that you simply save the web map.
Since the bad layer is not loading or showing up in the web map, when you save it, it will no longer try to connect to the feature service in question.
Alternative: (Only To Be Done By Advanced Users)
If you still have an issue, then in Admin Tools Pro, export the web map to CSV (including the JSON / Text column), open it in a text editor, and remove the JSON value for the broken feature service. The exact field to export / edit is: "JSON Data (text)"
After removing the JSON value for the broken feature service, Import the edited CSV.
NOTE: Again, this should only be done by advanced users, and we recommend making a backup of the original export before editing the JSON or even opening it in any editor.