The proper way to troubleshoot this would be to look a the ArcGIS Server Logs. (In Verbose level if need be)
The stopping COULD be the inability to access/write to the Config-store files. Where are the config-store files? on a NAS? SAN? Local?
One option i would be to STOP ArcGIS Server Windows Service and then restart... this would release the .rlock files not allowing stopping a service. (or the service is actually stopped) but the browser web interface cant get the proper status from ArcGIS Server.
It would NOT be any of these:
- TCP chimney
- TCP RSS
- Open ports from 16383 to 500 or Default.
4 Change DNS servers