I have a single instance where a member of the public is trying to access a web map and getting this error. This person is completely outside my organization. I have been unable to replicate it, despite testing the map across multiple browsers on multiple computers and my phone. I recommended refreshing the map and clearing their cache, which they said they did and are still having problems. The layer in question is a hosted feature layer on ArcGIS Online and is publicly shared. I am suspecting a firewall or other security issue thanks to this blog, but that doesn't help me help them.
Inspecting the network traffic will be the best way to determine what the problem is. Either install Fiddler or use the browsers developer tools to determine what request is failing by looking at the response codes and body of the response.