We had a similar situation too in version 10.31. Three errors would generate every minute
Our solution was similar to Alex, except we were unable to remove the server from the site so we did the following:
Using the admin utility, unregister the problem server
On the problem server bring up services and restart the ArcGIS server service
Using arcgis manager, add it as a machine - it took about 5-6 minutes to process and it added it as a machine and to the cluster