I have a map service that has many layers (probably too many), and the "Configure Popups" option simply does not work. Nothing happens when I select it. Does it stop working when a map service has too many layers? I restarted the browser (Chrome). Rebooted the machine.
I had this happen to me once with an external service. It turned out there was something wrong with the service. I had a web map where I could configure the popups in layers in other services, but after I tried to configure a popup with the problem service, I couldn't configure any layers in any service.
I opened a ticket with Esri, but since this was a service owned by someone else, they couldn't fix it. Unfortunately, I couldn't find a contact person for that service to see what was wrong.
The number of layers in a map service should not prevent pop-ups in a web map from working. However, when working with many layers, the layer ID can get messed up if layers within the map are shifted around when overwriting the service, which can cause issues with pop-ups. More info can be found in this doc: Problem: Pop-ups for feature layers in a web map are switched after overwriting a feature service
Try the solution in the doc above. If you are using ArcGIS Pro, use this: Introduction to sharing web layers—ArcGIS Pro | Documentation
Once the service is republished, add it to a new web map and attempt to configure pop-ups