When troubleshooting the communication between Management Point and the Clients we should use the following log files which resides on client computers.
1. Location Services.log : This log file show us client activity for locating management points, software update points, and distribution points.
2. ClientLocations.log: This log file show us the activity that are related to client site assignment
You can check the health of your Management Point by testing the following links also. If you can see the xml outputs like below pictures. Client and MP connectivity is healthy. Otherwise, you will see Error messages.